Package TEES :: Package Utils :: Package STFormat :: Module Scores
[hide private]

Module Scores

source code

Functions [hide private]
 
getResults(results) source code
 
getScoreDict(scoreString)
Extract individual scores from a comma-separated list
source code
 
updateRange(rangeDict, sourceDict) source code
 
getRangeDicts(documents) source code
 
getStatValues(documents) source code
 
standardize(score, statValues, scoreType) source code
 
getEventEVEXScore(event, statValues) source code
 
getScore(scoreDict, typeString=None)
Get the highest score (optionally for a known type)
source code
 
normalizeScore(value, key, rangeDict) source code
 
processScores(documents, normalize=False)
Convert score strings to a single float value
source code
 
sortByScore(documents, sortMethod='unmerging')
Make an ordered list for all events in all documents
source code
 
markForRemoval(eventList, cutoff=1.0)
Take an ordered event list, and mark a fraction for removal by setting their arguments to [], thus causing them to be removed in validation.
source code
 
evaluate(documents, sortMethod, verbose, cutoffs=[], task='GE.2') source code
 
resultsToGraph(results, outputname, maxEvents=None, manualEvaluationFile=None, graphs='prf') source code
 
getManualEvaluationPrecisions(manualEvaluationFile) source code
 
plotManualEvaluationPrecisions(precisions, binSize=1, makeFig=True) source code
 
beta(a, b, size=None)
The Beta distribution over ``[0, 1]``.
source code
 
binomial(n, p, size=None)
Draw samples from a binomial distribution.
source code
 
bytes(length)
Return random bytes.
source code
 
chisquare(df, size=None)
Draw samples from a chi-square distribution.
source code
 
exponential(scale=1.0, size=None)
Exponential distribution.
source code
 
f(dfnum, dfden, size=None)
Draw samples from a F distribution.
source code
 
gamma(shape, scale=1.0, size=None)
Draw samples from a Gamma distribution.
source code
 
geometric(p, size=None)
Draw samples from the geometric distribution.
source code
 
get_state()
Return a tuple representing the internal state of the generator.
source code
 
gumbel(loc=0.0, scale=1.0, size=None)
Gumbel distribution.
source code
 
hypergeometric(ngood, nbad, nsample, size=None)
Draw samples from a Hypergeometric distribution.
source code
 
laplace(loc=0.0, scale=1.0, size=None)
Laplace or double exponential distribution.
source code
 
logistic(loc=0.0, scale=1.0, size=None)
Draw samples from a Logistic distribution.
source code
 
lognormal(mean=0.0, sigma=1.0, size=None)
Return samples drawn from a log-normal distribution.
source code
 
logseries(p, size=None)
Draw samples from a Logarithmic Series distribution.
source code
 
multinomial(n, pvals, size=None)
Draw samples from a multinomial distribution.
source code
 
multivariate_normal(mean, cov, size=...)
Draw random samples from a multivariate normal distribution.
source code
 
negative_binomial(n, p, size=None)
Negative Binomial distribution.
source code
 
noncentral_chisquare(df, nonc, size=None)
Draw samples from a noncentral chi-square distribution.
source code
 
noncentral_f(dfnum, dfden, nonc, size=None)
Noncentral F distribution.
source code
 
normal(loc=0.0, scale=1.0, size=None)
Draw random samples from a normal (Gaussian) distribution.
source code
 
pareto(a, size=None)
Draw samples from a Pareto distribution with specified shape.
source code
 
permutation(x)
Randomly permute a sequence, or return a permuted range.
source code
 
poisson(lam=1.0, size=None)
Poisson distribution.
source code
 
power(a, size=None)
Power distribution.
source code
 
rand(d0, d1, dn, ...)
Random values in a given shape.
source code
 
randint(low, high=None, size=None)
Return random integers x such that low <= x < high.
source code
 
randn(d0, d1, dn, ...)
Returns zero-mean, unit-variance Gaussian random numbers in an array of shape (d0, d1, ..., dn).
source code
 
random_integers(low, high=None, size=None)
Return random integers x such that low <= x <= high.
source code
 
random_sample(size=None)
Return random floats in the half-open interval [0.0, 1.0).
source code
 
rayleigh(scale=1.0, size=None)
Rayleigh distribution.
source code
 
seed(seed=None)
Seed the generator.
source code
 
set_state(state)
Set the state from a tuple.
source code
 
shuffle(x)
Modify a sequence in-place by shuffling its contents.
source code
 
standard_cauchy(size=None)
Standard Cauchy with mode=0.
source code
 
standard_exponential(size=None)
Standard exponential distribution (scale=1).
source code
 
standard_gamma(shape, size=None)
Standard Gamma distribution.
source code
 
standard_normal(size=None)
Returns samples from a Standard Normal distribution (mean=0, stdev=1).
source code
 
standard_t(df, size=None)
Standard Student's t distribution with df degrees of freedom.
source code
 
triangular(left, mode, right, size=None)
Triangular distribution starting at left, peaking at mode, and ending at right (left <= mode <= right).
source code
 
uniform(low=0.0, high=1.0, size=1)
Draw samples from a uniform distribution.
source code
 
vonmises(mu=0.0, kappa=1.0, size=None)
Draw samples from a von Mises distribution.
source code
 
wald(mean, scale, size=None)
Wald (inverse Gaussian) distribution.
source code
 
weibull(a, size=None)
Weibull distribution.
source code
 
zipf(a, size=None)
Draw samples from a Zipf distribution.
source code
Variables [hide private]
  thisPath = '/home/jari/TEES/Utils/STFormat'
  ALLOW_THREADS = 1
  BUFSIZE = 10000
  CLIP = 0
  ERR_CALL = 3
  ERR_DEFAULT = 0
  ERR_DEFAULT2 = 2084
  ERR_IGNORE = 0
  ERR_LOG = 5
  ERR_PRINT = 4
  ERR_RAISE = 2
  ERR_WARN = 1
  FLOATING_POINT_SUPPORT = 1
  FPE_DIVIDEBYZERO = 1
  FPE_INVALID = 8
  FPE_OVERFLOW = 2
  FPE_UNDERFLOW = 4
  False_ = False
  Inf = inf
  Infinity = inf
  MAXDIMS = 32
  NAN = nan
  NINF = -inf
  NZERO = -0.0
  NaN = nan
  PINF = inf
  PZERO = 0.0
  RAISE = 2
  SHIFT_DIVIDEBYZERO = 0
  SHIFT_INVALID = 9
  SHIFT_OVERFLOW = 3
  SHIFT_UNDERFLOW = 6
  ScalarType = (<type 'int'>, <type 'float'>, <type 'complex'>, ...
  True_ = True
  UFUNC_BUFSIZE_DEFAULT = 10000
  UFUNC_PYVALS_NAME = 'UFUNC_PYVALS'
  WRAP = 1
  __package__ = 'TEES.Utils.STFormat'
  absolute = <ufunc 'absolute'>
  add = <ufunc 'add'>
  arccos = <ufunc 'arccos'>
  arccosh = <ufunc 'arccosh'>
  arcsin = <ufunc 'arcsin'>
  arcsinh = <ufunc 'arcsinh'>
  arctan = <ufunc 'arctan'>
  arctan2 = <ufunc 'arctan2'>
  arctanh = <ufunc 'arctanh'>
  bitwise_and = <ufunc 'bitwise_and'>
  bitwise_not = <ufunc 'invert'>
  bitwise_or = <ufunc 'bitwise_or'>
  bitwise_xor = <ufunc 'bitwise_xor'>
  c_ = <numpy.lib.index_tricks.CClass object at 0xaaa824c>
  cast = {<type 'numpy.int64'>: <function <lambda> at 0xa9a741c>...
  ceil = <ufunc 'ceil'>
  conj = <ufunc 'conjugate'>
  conjugate = <ufunc 'conjugate'>
  cos = <ufunc 'cos'>
  cosh = <ufunc 'cosh'>
  deg2rad = <ufunc 'deg2rad'>
  degrees = <ufunc 'degrees'>
  divide = <ufunc 'divide'>
  e = 2.71828182846
  equal = <ufunc 'equal'>
  exp = <ufunc 'exp'>
  exp2 = <ufunc 'exp2'>
  expm1 = <ufunc 'expm1'>
  fabs = <ufunc 'fabs'>
  floor = <ufunc 'floor'>
  floor_divide = <ufunc 'floor_divide'>
  fmax = <ufunc 'fmax'>
  fmin = <ufunc 'fmin'>
  fmod = <ufunc 'fmod'>
  frexp = <ufunc 'frexp'>
  greater = <ufunc 'greater'>
  greater_equal = <ufunc 'greater_equal'>
  hypot = <ufunc 'hypot'>
  index_exp = <numpy.lib.index_tricks.IndexExpression object at ...
  inf = inf
  infty = inf
  invert = <ufunc 'invert'>
  isfinite = <ufunc 'isfinite'>
  isinf = <ufunc 'isinf'>
  isnan = <ufunc 'isnan'>
  ldexp = <ufunc 'ldexp'>
  left_shift = <ufunc 'left_shift'>
  less = <ufunc 'less'>
  less_equal = <ufunc 'less_equal'>
  little_endian = True
  log = <ufunc 'log'>
  log10 = <ufunc 'log10'>
  log1p = <ufunc 'log1p'>
  logaddexp = <ufunc 'logaddexp'>
  logaddexp2 = <ufunc 'logaddexp2'>
  logical_and = <ufunc 'logical_and'>
  logical_not = <ufunc 'logical_not'>
  logical_or = <ufunc 'logical_or'>
  logical_xor = <ufunc 'logical_xor'>
  maximum = <ufunc 'maximum'>
  mgrid = <numpy.lib.index_tricks.nd_grid object at 0xaaa812c>
  minimum = <ufunc 'minimum'>
  mod = <ufunc 'remainder'>
  modf = <ufunc 'modf'>
  multiply = <ufunc 'multiply'>
  nan = nan
  nbytes = {<type 'numpy.int64'>: 8, <type 'numpy.int16'>: 2, <t...
  negative = <ufunc 'negative'>
  newaxis = None
  not_equal = <ufunc 'not_equal'>
  ogrid = <numpy.lib.index_tricks.nd_grid object at 0xaaa814c>
  ones_like = <ufunc 'ones_like'>
  pi = 3.14159265359
  r_ = <numpy.lib.index_tricks.RClass object at 0xaaa81cc>
  rad2deg = <ufunc 'rad2deg'>
  radians = <ufunc 'radians'>
  reciprocal = <ufunc 'reciprocal'>
  remainder = <ufunc 'remainder'>
  right_shift = <ufunc 'right_shift'>
  rint = <ufunc 'rint'>
  s_ = <numpy.lib.index_tricks.IndexExpression object at 0xaaa83ec>
  sctypeDict = {0: <type 'numpy.bool_'>, 1: <type 'numpy.int8'>,...
  sctypeNA = {'?': 'Bool', 'B': 'UInt8', 'Bool': <type 'numpy.bo...
  sctypes = {'complex': [<type 'numpy.complex64'>, <type 'numpy....
  sign = <ufunc 'sign'>
  signbit = <ufunc 'signbit'>
  sin = <ufunc 'sin'>
  sinh = <ufunc 'sinh'>
  sqrt = <ufunc 'sqrt'>
  square = <ufunc 'square'>
  subtract = <ufunc 'subtract'>
  tan = <ufunc 'tan'>
  tanh = <ufunc 'tanh'>
  true_divide = <ufunc 'true_divide'>
  trunc = <ufunc 'trunc'>
  typeDict = {0: <type 'numpy.bool_'>, 1: <type 'numpy.int8'>, 2...
  typeNA = {'?': 'Bool', 'B': 'UInt8', 'Bool': <type 'numpy.bool...
  typecodes = {'All': '?bhilqpBHILQPfdgFDGSUVO', 'AllFloat': 'fd...
Function Details [hide private]

beta(a, b, size=None)

source code 
The Beta distribution over ``[0, 1]``.

The Beta distribution is a special case of the Dirichlet distribution,
and is related to the Gamma distribution.  It has the probability
distribution function

.. math:: f(x; a,b) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1}
                                                 (1 - x)^{\beta - 1},

where the normalisation, B, is the beta function,

.. math:: B(\alpha, \beta) = \int_0^1 t^{\alpha - 1}
                             (1 - t)^{\beta - 1} dt.

It is often seen in Bayesian inference and order statistics.

Parameters
----------
a : float
    Alpha, non-negative.
b : float
    Beta, non-negative.
size : tuple of ints, optional
    The number of samples to draw.  The ouput is packed according to
    the size given.

Returns
-------
out : ndarray
    Array of the given shape, containing values drawn from a
    Beta distribution.

binomial(n, p, size=None)

source code 
Draw samples from a binomial distribution.

Samples are drawn from a Binomial distribution with specified
parameters, n trials and p probability of success where
n an integer > 0 and p is in the interval [0,1]. (n may be
input as a float, but it is truncated to an integer in use)

Parameters
----------
n : float (but truncated to an integer)
        parameter, > 0.
p : float
        parameter, >= 0 and <=1.
size : {tuple, int}
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
samples : {ndarray, scalar}
          where the values are all integers in  [0, n].

See Also
--------
scipy.stats.distributions.binom : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Binomial distribution is

.. math:: P(N) = \binom{n}{N}p^N(1-p)^{n-N},

where :math:`n` is the number of trials, :math:`p` is the probability
of success, and :math:`N` is the number of successes.

When estimating the standard error of a proportion in a population by
using a random sample, the normal distribution works well unless the
product p*n <=5, where p = population proportion estimate, and n =
number of samples, in which case the binomial distribution is used
instead. For example, a sample of 15 people shows 4 who are left
handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,
so the binomial distribution should be used in this case.

References
----------
.. [1] Dalgaard, Peter, "Introductory Statistics with R",
       Springer-Verlag, 2002.
.. [2] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
       Fifth Edition, 2002.
.. [3] Lentner, Marvin, "Elementary Applied Statistics", Bogden
       and Quigley, 1972.
.. [4] Weisstein, Eric W. "Binomial Distribution." From MathWorld--A
       Wolfram Web Resource.
       http://mathworld.wolfram.com/BinomialDistribution.html
.. [5] Wikipedia, "Binomial-distribution",
       http://en.wikipedia.org/wiki/Binomial_distribution

Examples
--------
Draw samples from the distribution:

>>> n, p = 10, .5 # number of trials, probability of each trial
>>> s = np.random.binomial(n, p, 1000)
# result of flipping a coin 10 times, tested 1000 times.

A real world example. A company drills 9 wild-cat oil exploration
wells, each with an estimated probability of success of 0.1. All nine
wells fail. What is the probability of that happening?

Let's do 20,000 trials of the model, and count the number that
generate zero positive results.

>>> sum(np.random.binomial(9,0.1,20000)==0)/20000.
answer = 0.38885, or 38%.

bytes(length)

source code 
Return random bytes.

Parameters
----------
length : int
    Number of random bytes.

Returns
-------
out : str
    String of length `N`.

Examples
--------
>>> np.random.bytes(10)
' eh\x85\x022SZ\xbf\xa4' #random

chisquare(df, size=None)

source code 
Draw samples from a chi-square distribution.

When `df` independent random variables, each with standard
normal distributions (mean 0, variance 1), are squared and summed,
the resulting distribution is chi-square (see Notes).  This
distribution is often used in hypothesis testing.

Parameters
----------
df : int
     Number of degrees of freedom.
size : tuple of ints, int, optional
     Size of the returned array.  By default, a scalar is
     returned.

Returns
-------
output : ndarray
    Samples drawn from the distribution, packed in a `size`-shaped
    array.

Raises
------
ValueError
    When `df` <= 0 or when an inappropriate `size` (e.g. ``size=-1``)
    is given.

Notes
-----
The variable obtained by summing the squares of `df` independent,
standard normally distributed random variables:

.. math:: Q = \sum_{i=0}^{\mathtt{df}} X^2_i

is chi-square distributed, denoted

.. math:: Q \sim \chi^2_k.

The probability density function of the chi-squared distribution is

.. math:: p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)}
                 x^{k/2 - 1} e^{-x/2},

where :math:`\Gamma` is the gamma function,

.. math:: \Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt.

References
----------
.. [1] NIST/SEMATECH e-Handbook of Statistical Methods,
       http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
.. [2] Wikipedia, "Chi-square distribution",
       http://en.wikipedia.org/wiki/Chi-square_distribution

Examples
--------
>>> np.random.chisquare(2,4)
array([ 1.89920014,  9.00867716,  3.13710533,  5.62318272])

exponential(scale=1.0, size=None)

source code 
Exponential distribution.

Its probability density function is

.. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),

for ``x > 0`` and 0 elsewhere. :math:`\beta` is the scale parameter,
which is the inverse of the rate parameter :math:`\lambda = 1/\beta`.
The rate parameter is an alternative, widely used parameterization
of the exponential distribution [3]_.

The exponential distribution is a continuous analogue of the
geometric distribution.  It describes many common situations, such as
the size of raindrops measured over many rainstorms [1]_, or the time
between page requests to Wikipedia [2]_.

Parameters
----------
scale : float
    The scale parameter, :math:`\beta = 1/\lambda`.
size : tuple of ints
    Number of samples to draw.  The output is shaped
    according to `size`.

References
----------
.. [1] Peyton Z. Peebles Jr., "Probability, Random Variables and
       Random Signal Principles", 4th ed, 2001, p. 57.
.. [2] "Poisson Process", Wikipedia,
       http://en.wikipedia.org/wiki/Poisson_process
.. [3] "Exponential Distribution, Wikipedia,
       http://en.wikipedia.org/wiki/Exponential_distribution

f(dfnum, dfden, size=None)

source code 
Draw samples from a F distribution.

Samples are drawn from an F distribution with specified parameters,
`dfnum` (degrees of freedom in numerator) and `dfden` (degrees of freedom
in denominator), where both parameters should be greater than zero.

The random variate of the F distribution (also known as the
Fisher distribution) is a continuous probability distribution
that arises in ANOVA tests, and is the ratio of two chi-square
variates.

Parameters
----------
dfnum : float
    Degrees of freedom in numerator. Should be greater than zero.
dfden : float
    Degrees of freedom in denominator. Should be greater than zero.
size : {tuple, int}, optional
    Output shape.  If the given shape is, e.g., ``(m, n, k)``,
    then ``m * n * k`` samples are drawn. By default only one sample
    is returned.

Returns
-------
samples : {ndarray, scalar}
    Samples from the Fisher distribution.

See Also
--------
scipy.stats.distributions.f : probability density function,
    distribution or cumulative density function, etc.

Notes
-----

The F statistic is used to compare in-group variances to between-group
variances. Calculating the distribution depends on the sampling, and
so it is a function of the respective degrees of freedom in the
problem.  The variable `dfnum` is the number of samples minus one, the
between-groups degrees of freedom, while `dfden` is the within-groups
degrees of freedom, the sum of the number of samples in each group
minus the number of groups.

References
----------
.. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
       Fifth Edition, 2002.
.. [2] Wikipedia, "F-distribution",
       http://en.wikipedia.org/wiki/F-distribution

Examples
--------
An example from Glantz[1], pp 47-40.
Two groups, children of diabetics (25 people) and children from people
without diabetes (25 controls). Fasting blood glucose was measured,
case group had a mean value of 86.1, controls had a mean value of
82.2. Standard deviations were 2.09 and 2.49 respectively. Are these
data consistent with the null hypothesis that the parents diabetic
status does not affect their children's blood glucose levels?
Calculating the F statistic from the data gives a value of 36.01.

Draw samples from the distribution:

>>> dfnum = 1. # between group degrees of freedom
>>> dfden = 48. # within groups degrees of freedom
>>> s = np.random.f(dfnum, dfden, 1000)

The lower bound for the top 1% of the samples is :

>>> sort(s)[-10]
7.61988120985

So there is about a 1% chance that the F statistic will exceed 7.62,
the measured value is 36, so the null hypothesis is rejected at the 1%
level.

gamma(shape, scale=1.0, size=None)

source code 
Draw samples from a Gamma distribution.

Samples are drawn from a Gamma distribution with specified parameters,
`shape` (sometimes designated "k") and `scale` (sometimes designated
"theta"), where both parameters are > 0.

Parameters
----------
shape : scalar > 0
    The shape of the gamma distribution.
scale : scalar > 0, optional
    The scale of the gamma distribution.  Default is equal to 1.
size : shape_tuple, optional
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
out : ndarray, float
    Returns one sample unless `size` parameter is specified.

See Also
--------
scipy.stats.distributions.gamma : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Gamma distribution is

.. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},

where :math:`k` is the shape and :math:`\theta` the scale,
and :math:`\Gamma` is the Gamma function.

The Gamma distribution is often used to model the times to failure of
electronic components, and arises naturally in processes for which the
waiting times between Poisson distributed events are relevant.

References
----------
.. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A
       Wolfram Web Resource.
       http://mathworld.wolfram.com/GammaDistribution.html
.. [2] Wikipedia, "Gamma-distribution",
       http://en.wikipedia.org/wiki/Gamma-distribution

Examples
--------
Draw samples from the distribution:

>>> shape, scale = 2., 2. # mean and dispersion
>>> s = np.random.gamma(shape, scale, 1000)

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> import scipy.special as sps
>>> count, bins, ignored = plt.hist(s, 50, normed=True)
>>> y = bins**(shape-1)*((exp(-bins/scale))/\
    (sps.gamma(shape)*scale**shape))
>>> plt.plot(bins, y, linewidth=2, color='r')
>>> plt.show()

geometric(p, size=None)

source code 
Draw samples from the geometric distribution.

Bernoulli trials are experiments with one of two outcomes:
success or failure (an example of such an experiment is flipping
a coin).  The geometric distribution models the number of trials
that must be run in order to achieve success.  It is therefore
supported on the positive integers, ``k = 1, 2, ...``.

The probability mass function of the geometric distribution is

.. math:: f(k) = (1 - p)^{k - 1} p

where `p` is the probability of success of an individual trial.

Parameters
----------
p : float
    The probability of success of an individual trial.
size : tuple of ints
    Number of values to draw from the distribution.  The output
    is shaped according to `size`.

Returns
-------
out : ndarray
    Samples from the geometric distribution, shaped according to
    `size`.

Examples
--------
Draw ten thousand values from the geometric distribution,
with the probability of an individual success equal to 0.35:

>>> z = np.random.geometric(p=0.35, size=10000)

How many trials succeeded after a single run?

>>> (z == 1).sum() / 10000.
0.34889999999999999 #random

get_state()

source code 
Return a tuple representing the internal state of the generator.

Returns
-------
out : tuple(string, list of 624 integers, int, int, float)
    The returned tuple has the following items:

    1. the string 'MT19937'
    2. a list of 624 integer keys
    3. an integer pos
    4. an integer has_gauss
    5. and a float cached_gaussian

See Also
--------
set_state

gumbel(loc=0.0, scale=1.0, size=None)

source code 
Gumbel distribution.

Draw samples from a Gumbel distribution with specified location (or mean)
and scale (or standard deviation).

The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value
Type I) distribution is one of a class of Generalized Extreme Value (GEV)
distributions used in modeling extreme value problems.  The Gumbel is a
special case of the Extreme Value Type I distribution for maximums from
distributions with "exponential-like" tails, it may be derived by
considering a Gaussian process of measurements, and generating the pdf for
the maximum values from that set of measurements (see examples).

Parameters
----------
loc : float
    The location of the mode of the distribution.
scale : float
    The scale parameter of the distribution.
size : tuple of ints
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

See Also
--------
scipy.stats.gumbel : probability density function,
    distribution or cumulative density function, etc.
weibull, scipy.stats.genextreme

Notes
-----
The probability density for the Gumbel distribution is

.. math:: p(x) = \frac{e^{-(x - \mu)/ \beta}}{\beta} e^{ -e^{-(x - \mu)/
          \beta}},

where :math:`\mu` is the mode, a location parameter, and :math:`\beta`
is the scale parameter.

The Gumbel (named for German mathematician Emil Julius Gumbel) was used
very early in the hydrology literature, for modeling the occurrence of
flood events. It is also used for modeling maximum wind speed and rainfall
rates.  It is a "fat-tailed" distribution - the probability of an event in
the tail of the distribution is larger than if one used a Gaussian, hence
the surprisingly frequent occurrence of 100-year floods. Floods were
initially modeled as a Gaussian process, which underestimated the frequency
of extreme events.

It is one of a class of extreme value distributions, the Generalized
Extreme Value (GEV) distributions, which also includes the Weibull and
Frechet.

The function has a mean of :math:`\mu + 0.57721\beta` and a variance of
:math:`\frac{\pi^2}{6}\beta^2`.

References
----------
.. [1] Gumbel, E.J. (1958). Statistics of Extremes. Columbia University
       Press.
.. [2] Reiss, R.-D. and Thomas M. (2001), Statistical Analysis of Extreme
       Values, from Insurance, Finance, Hydrology and Other Fields,
       Birkhauser Verlag, Basel: Boston : Berlin.
.. [3] Wikipedia, "Gumbel distribution",
       http://en.wikipedia.org/wiki/Gumbel_distribution

Examples
--------
Draw samples from the distribution:

>>> mu, beta = 0, 0.1 # location and scale
>>> s = np.random.gumbel(mu, beta, 1000)

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 30, normed=True)
>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)
...          * np.exp( -np.exp( -(bins - mu) /beta) ),
...          linewidth=2, color='r')
>>> plt.show()

Show how an extreme value distribution can arise from a Gaussian process
and compare to a Gaussian:

>>> means = []
>>> maxima = []
>>> for i in range(0,1000) :
...    a = np.random.normal(mu, beta, 1000)
...    means.append(a.mean())
...    maxima.append(a.max())
>>> count, bins, ignored = plt.hist(maxima, 30, normed=True)
>>> beta = np.std(maxima)*np.pi/np.sqrt(6)
>>> mu = np.mean(maxima) - 0.57721*beta
>>> plt.plot(bins, (1/beta)*np.exp(-(bins - mu)/beta)
...          * np.exp(-np.exp(-(bins - mu)/beta)),
...          linewidth=2, color='r')
>>> plt.plot(bins, 1/(beta * np.sqrt(2 * np.pi))
...          * np.exp(-(bins - mu)**2 / (2 * beta**2)),
...          linewidth=2, color='g')
>>> plt.show()

hypergeometric(ngood, nbad, nsample, size=None)

source code 
Draw samples from a Hypergeometric distribution.

Samples are drawn from a Hypergeometric distribution with specified
parameters, ngood (ways to make a good selection), nbad (ways to make
a bad selection), and nsample = number of items sampled, which is less
than or equal to the sum ngood + nbad.

Parameters
----------
ngood : float (but truncated to an integer)
        parameter, > 0.
nbad  : float
        parameter, >= 0.
nsample  : float
           parameter, > 0 and <= ngood+nbad
size : {tuple, int}
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
samples : {ndarray, scalar}
          where the values are all integers in  [0, n].

See Also
--------
scipy.stats.distributions.hypergeom : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Hypergeometric distribution is

.. math:: P(x) = \frac{\binom{m}{n}\binom{N-m}{n-x}}{\binom{N}{n}},

where :math:`0 \le x \le m` and :math:`n+m-N \le x \le n`

for P(x) the probability of x successes, n = ngood, m = nbad, and
N = number of samples.

Consider an urn with black and white marbles in it, ngood of them
black and nbad are white. If you draw nsample balls without
replacement, then the Hypergeometric distribution describes the
distribution of black balls in the drawn sample.

Note that this distribution is very similar to the Binomial
distribution, except that in this case, samples are drawn without
replacement, whereas in the Binomial case samples are drawn with
replacement (or the sample space is infinite). As the sample space
becomes large, this distribution approaches the Binomial.

References
----------
.. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden
       and Quigley, 1972.
.. [2] Weisstein, Eric W. "Hypergeometric Distribution." From
       MathWorld--A Wolfram Web Resource.
       http://mathworld.wolfram.com/HypergeometricDistribution.html
.. [3] Wikipedia, "Hypergeometric-distribution",
       http://en.wikipedia.org/wiki/Hypergeometric-distribution

Examples
--------
Draw samples from the distribution:

>>> ngood, nbad, nsamp = 100, 2, 10
# number of good, number of bad, and number of samples
>>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000)
>>> hist(s)
#   note that it is very unlikely to grab both bad items

Suppose you have an urn with 15 white and 15 black marbles.
If you pull 15 marbles at random, how likely is it that
12 or more of them are one color?

>>> s = np.random.hypergeometric(15, 15, 15, 100000)
>>> sum(s>=12)/100000. + sum(s<=3)/100000.
#   answer = 0.003 ... pretty unlikely!

laplace(loc=0.0, scale=1.0, size=None)

source code 
Laplace or double exponential distribution.

It has the probability density function

.. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda}
                               \exp\left(-\frac{|x - \mu|}{\lambda}\right).

The Laplace distribution is similar to the Gaussian/normal distribution,
but is sharper at the peak and has fatter tails.

Parameters
----------
loc : float
    The position, :math:`\mu`, of the distribution peak.
scale : float
    :math:`\lambda`, the exponential decay.

logistic(loc=0.0, scale=1.0, size=None)

source code 
Draw samples from a Logistic distribution.

Samples are drawn from a Logistic distribution with specified
parameters, loc (location or mean, also median), and scale (>0).

Parameters
----------
loc : float

scale : float > 0.

size : {tuple, int}
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
samples : {ndarray, scalar}
          where the values are all integers in  [0, n].

See Also
--------
scipy.stats.distributions.logistic : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Logistic distribution is

.. math:: P(x) = P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2},

where :math:`\mu` = location and :math:`s` = scale.

The Logistic distribution is used in Extreme Value problems where it
can act as a mixture of Gumbel distributions, in Epidemiology, and by
the World Chess Federation (FIDE) where it is used in the Elo ranking
system, assuming the performance of each player is a logistically
distributed random variable.

References
----------
.. [1] Reiss, R.-D. and Thomas M. (2001), Statistical Analysis of Extreme
       Values, from Insurance, Finance, Hydrology and Other Fields,
       Birkhauser Verlag, Basel, pp 132-133.
.. [2] Weisstein, Eric W. "Logistic Distribution." From
       MathWorld--A Wolfram Web Resource.
       http://mathworld.wolfram.com/LogisticDistribution.html
.. [3] Wikipedia, "Logistic-distribution",
       http://en.wikipedia.org/wiki/Logistic-distribution

Examples
--------
Draw samples from the distribution:

>>> loc, scale = 10, 1
>>> s = np.random.logistic(loc, scale, 10000)
>>> count, bins, ignored = plt.hist(s, bins=50)

#   plot against distribution

>>> def logist(x, loc, scale):
...     return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2)
>>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\
... logist(bins, loc, scale).max())
>>> plt.show()

lognormal(mean=0.0, sigma=1.0, size=None)

source code 
Return samples drawn from a log-normal distribution.

Draw samples from a log-normal distribution with specified mean, standard
deviation, and shape. Note that the mean and standard deviation are not the
values for the distribution itself, but of the underlying normal
distribution it is derived from.


Parameters
----------
mean : float
    Mean value of the underlying normal distribution
sigma : float, >0.
    Standard deviation of the underlying normal distribution
size : tuple of ints
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

See Also
--------
scipy.stats.lognorm : probability density function, distribution,
    cumulative density function, etc.

Notes
-----
A variable `x` has a log-normal distribution if `log(x)` is normally
distributed.

The probability density function for the log-normal distribution is

.. math:: p(x) = \frac{1}{\sigma x \sqrt{2\pi}}
                 e^{(-\frac{(ln(x)-\mu)^2}{2\sigma^2})}

where :math:`\mu` is the mean and :math:`\sigma` is the standard deviation
of the normally distributed logarithm of the variable.

A log-normal distribution results if a random variable is the *product* of
a large number of independent, identically-distributed variables in the
same way that a normal distribution results if the variable is the *sum*
of a large number of independent, identically-distributed variables
(see the last example). It is one of the so-called "fat-tailed"
distributions.

The log-normal distribution is commonly used to model the lifespan of units
with fatigue-stress failure modes. Since this includes
most mechanical systems, the log-normal distribution has widespread
application.

It is also commonly used to model oil field sizes, species abundance, and
latent periods of infectious diseases.

References
----------
.. [1] Eckhard Limpert, Werner A. Stahel, and Markus Abbt, "Log-normal
       Distributions across the Sciences: Keys and Clues", May 2001
       Vol. 51 No. 5 BioScience
       http://stat.ethz.ch/~stahel/lognormal/bioscience.pdf
.. [2] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme
       Values, Birkhauser Verlag, Basel, pp 31-32.
.. [3] Wikipedia, "Lognormal distribution",
       http://en.wikipedia.org/wiki/Lognormal_distribution

Examples
--------
Draw samples from the distribution:

>>> mu, sigma = 3., 1. # mean and standard deviation
>>> s = np.random.lognormal(mu, sigma, 1000)

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 100, normed=True, align='center')

>>> x = np.linspace(min(bins), max(bins), 10000)
>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))
...        / (x * sigma * np.sqrt(2 * np.pi)))

>>> plt.plot(x, pdf, linewidth=2, color='r')
>>> plt.axis('tight')
>>> plt.show()

Demonstrate that taking the products of random samples from a uniform
distribution can be fit well by a log-normal probability density function.

>>> # Generate a thousand samples: each is the product of 100 random
>>> # values, drawn from a normal distribution.
>>> b = []
>>> for i in range(1000):
...    a = 10. + np.random.random(100)
...    b.append(np.product(a))

>>> b = np.array(b) / np.min(b) # scale values to be positive

>>> count, bins, ignored = plt.hist(b, 100, normed=True, align='center')

>>> sigma = np.std(np.log(b))
>>> mu = np.mean(np.log(b))

>>> x = np.linspace(min(bins), max(bins), 10000)
>>> pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))
...        / (x * sigma * np.sqrt(2 * np.pi)))

>>> plt.plot(x, pdf, color='r', linewidth=2)
>>> plt.show()

logseries(p, size=None)

source code 
Draw samples from a Logarithmic Series distribution.

Samples are drawn from a Log Series distribution with specified
parameter, p (probability, 0 < p < 1).

Parameters
----------
loc : float

scale : float > 0.

size : {tuple, int}
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
samples : {ndarray, scalar}
          where the values are all integers in  [0, n].

See Also
--------
scipy.stats.distributions.logser : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Log Series distribution is

.. math:: P(k) = \frac{-p^k}{k \ln(1-p)},

where p = probability.

The Log Series distribution is frequently used to represent species
richness and occurrence, first proposed by Fisher, Corbet, and
Williams in 1943 [2].  It may also be used to model the numbers of
occupants seen in cars [3].

References
----------
.. [1] Buzas, Martin A.; Culver, Stephen J.,  Understanding regional
       species diversity through the log series distribution of
       occurrences: BIODIVERSITY RESEARCH Diversity & Distributions,
       Volume 5, Number 5, September 1999 , pp. 187-195(9).
.. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The
       relation between the number of species and the number of
       individuals in a random sample of an animal population.
       Journal of Animal Ecology, 12:42-58.
.. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small
       Data Sets, CRC Press, 1994.
.. [4] Wikipedia, "Logarithmic-distribution",
       http://en.wikipedia.org/wiki/Logarithmic-distribution

Examples
--------
Draw samples from the distribution:

>>> a = .6
>>> s = np.random.logseries(a, 10000)
>>> count, bins, ignored = plt.hist(s)

#   plot against distribution

>>> def logseries(k, p):
...     return -p**k/(k*log(1-p))
>>> plt.plot(bins, logseries(bins, a)*count.max()/\
    logseries(bins, a).max(),'r')
>>> plt.show()

multinomial(n, pvals, size=None)

source code 
Draw samples from a multinomial distribution.

The multinomial distribution is a multivariate generalisation of the
binomial distribution.  Take an experiment with one of ``p``
possible outcomes.  An example of such an experiment is throwing a dice,
where the outcome can be 1 through 6.  Each sample drawn from the
distribution represents `n` such experiments.  Its values,
``X_i = [X_0, X_1, ..., X_p]``, represent the number of times the outcome
was ``i``.

Parameters
----------
n : int
    Number of experiments.
pvals : sequence of floats, length p
    Probabilities of each of the ``p`` different outcomes.  These
    should sum to 1 (however, the last element is always assumed to
    account for the remaining probability, as long as
    ``sum(pvals[:-1]) <= 1)``.
size : tuple of ints
    Given a `size` of ``(M, N, K)``, then ``M*N*K`` samples are drawn,
    and the output shape becomes ``(M, N, K, p)``, since each sample
    has shape ``(p,)``.

Examples
--------
Throw a dice 20 times:

>>> np.random.multinomial(20, [1/6.]*6, size=1)
array([[4, 1, 7, 5, 2, 1]])

It landed 4 times on 1, once on 2, etc.

Now, throw the dice 20 times, and 20 times again:

>>> np.random.multinomial(20, [1/6.]*6, size=2)
array([[3, 4, 3, 3, 4, 3],
       [2, 4, 3, 4, 0, 7]])

For the first run, we threw 3 times 1, 4 times 2, etc.  For the second,
we threw 2 times 1, 4 times 2, etc.

A loaded dice is more likely to land on number 6:

>>> np.random.multinomial(100, [1/7.]*5)
array([13, 16, 13, 16, 42])

multivariate_normal(mean, cov, size=...)

source code 
Draw random samples from a multivariate normal distribution.

The multivariate normal, multinormal or Gaussian distribution is a
generalisation of the one-dimensional normal distribution to higher
dimensions.

Such a distribution is specified by its mean and covariance matrix,
which are analogous to the mean (average or "centre") and variance
(standard deviation squared or "width") of the one-dimensional normal
distribution.

Parameters
----------
mean : (N,) ndarray
    Mean of the N-dimensional distribution.
cov : (N,N) ndarray
    Covariance matrix of the distribution.
size : tuple of ints, optional
    Given a shape of, for example, (m,n,k), m*n*k samples are
    generated, and packed in an m-by-n-by-k arrangement.  Because each
    sample is N-dimensional, the output shape is (m,n,k,N).  If no
    shape is specified, a single sample is returned.

Returns
-------
out : ndarray
    The drawn samples, arranged according to `size`.  If the
    shape given is (m,n,...), then the shape of `out` is is
    (m,n,...,N).

    In other words, each entry ``out[i,j,...,:]`` is an N-dimensional
    value drawn from the distribution.

Notes
-----
The mean is a coordinate in N-dimensional space, which represents the
location where samples are most likely to be generated.  This is
analogous to the peak of the bell curve for the one-dimensional or
univariate normal distribution.

Covariance indicates the level to which two variables vary together.
From the multivariate normal distribution, we draw N-dimensional
samples, :math:`X = [x_1, x_2, ... x_N]`.  The covariance matrix
element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`.
The element :math:`C_{ii}` is the variance of :math:`x_i` (i.e. its
"spread").

Instead of specifying the full covariance matrix, popular
approximations include:

  - Spherical covariance (`cov` is a multiple of the identity matrix)
  - Diagonal covariance (`cov` has non-negative elements, and only on
    the diagonal)

This geometrical property can be seen in two dimensions by plotting
generated data-points:

>>> mean = [0,0]
>>> cov = [[1,0],[0,100]] # diagonal covariance, points lie on x or y-axis

>>> import matplotlib.pyplot as plt
>>> x,y = np.random.multivariate_normal(mean,cov,5000).T
>>> plt.plot(x,y,'x'); plt.axis('equal'); plt.show()

Note that the covariance matrix must be non-negative definite.

References
----------
.. [1] A. Papoulis, "Probability, Random Variables, and Stochastic
       Processes," 3rd ed., McGraw-Hill Companies, 1991
.. [2] R.O. Duda, P.E. Hart, and D.G. Stork, "Pattern Classification,"
       2nd ed., Wiley, 2001.

Examples
--------
>>> mean = (1,2)
>>> cov = [[1,0],[1,0]]
>>> x = np.random.multivariate_normal(mean,cov,(3,3))
>>> x.shape
(3, 3, 2)

The following is probably true, given that 0.6 is roughly twice the
standard deviation:

>>> print list( (x[0,0,:] - mean) < 0.6 )
[True, True]

noncentral_chisquare(df, nonc, size=None)

source code 
Draw samples from a noncentral chi-square distribution.

The noncentral :math:`\chi^2` distribution is a generalisation of
the :math:`\chi^2` distribution.

Parameters
----------
df : int
    Degrees of freedom.
nonc : float
    Non-centrality.
size : tuple of ints
    Shape of the output.

normal(loc=0.0, scale=1.0, size=None)

source code 
Draw random samples from a normal (Gaussian) distribution.

The probability density function of the normal distribution, first
derived by De Moivre and 200 years later by both Gauss and Laplace
independently [2]_, is often called the bell curve because of
its characteristic shape (see the example below).

The normal distributions occurs often in nature.  For example, it
describes the commonly occurring distribution of samples influenced
by a large number of tiny, random disturbances, each with its own
unique distribution [2]_.

Parameters
----------
loc : float
    Mean ("centre") of the distribution.
scale : float
    Standard deviation (spread or "width") of the distribution.
size : tuple of ints
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

See Also
--------
scipy.stats.distributions.norm : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Gaussian distribution is

.. math:: p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }}
                 e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} },

where :math:`\mu` is the mean and :math:`\sigma` the standard deviation.
The square of the standard deviation, :math:`\sigma^2`, is called the
variance.

The function has its peak at the mean, and its "spread" increases with
the standard deviation (the function reaches 0.607 times its maximum at
:math:`x + \sigma` and :math:`x - \sigma` [2]_).  This implies that
`numpy.random.normal` is more likely to return samples lying close to the
mean, rather than those far away.

References
----------
.. [1] Wikipedia, "Normal distribution",
       http://en.wikipedia.org/wiki/Normal_distribution
.. [2] P. R. Peebles Jr., "Central Limit Theorem" in "Probability, Random
       Variables and Random Signal Principles", 4th ed., 2001,
       pp. 51, 51, 125.

Examples
--------
Draw samples from the distribution:

>>> mu, sigma = 0, 0.1 # mean and standard deviation
>>> s = np.random.normal(mu, sigma, 1000)

Verify the mean and the variance:

>>> abs(mu - np.mean(s)) < 0.01
True

>>> abs(sigma - np.std(s, ddof=1)) < 0.01
True

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 30, normed=True)
>>> plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *
...                np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
...          linewidth=2, color='r')
>>> plt.show()

pareto(a, size=None)

source code 
Draw samples from a Pareto distribution with specified shape.

This is a simplified version of the Generalized Pareto distribution
(available in SciPy), with the scale set to one and the location set to
zero. Most authors default the location to one.

The Pareto distribution must be greater than zero, and is unbounded above.
It is also known as the "80-20 rule".  In this distribution, 80 percent of
the weights are in the lowest 20 percent of the range, while the other 20
percent fill the remaining 80 percent of the range.

Parameters
----------
shape : float, > 0.
    Shape of the distribution.
size : tuple of ints
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

See Also
--------
scipy.stats.distributions.genpareto.pdf : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Pareto distribution is

.. math:: p(x) = \frac{am^a}{x^{a+1}}

where :math:`a` is the shape and :math:`m` the location

The Pareto distribution, named after the Italian economist Vilfredo Pareto,
is a power law probability distribution useful in many real world problems.
Outside the field of economics it is generally referred to as the Bradford
distribution. Pareto developed the distribution to describe the
distribution of wealth in an economy.  It has also found use in insurance,
web page access statistics, oil field sizes, and many other problems,
including the download frequency for projects in Sourceforge [1].  It is
one of the so-called "fat-tailed" distributions.


References
----------
.. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of
       Sourceforge projects.
.. [2] Pareto, V. (1896). Course of Political Economy. Lausanne.
.. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme
       Values, Birkhauser Verlag, Basel, pp 23-30.
.. [4] Wikipedia, "Pareto distribution",
       http://en.wikipedia.org/wiki/Pareto_distribution

Examples
--------
Draw samples from the distribution:

>>> a, m = 3., 1. # shape and mode
>>> s = np.random.pareto(a, 1000) + m

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 100, normed=True, align='center')
>>> fit = a*m**a/bins**(a+1)
>>> plt.plot(bins, max(count)*fit/max(fit),linewidth=2, color='r')
>>> plt.show()

permutation(x)

source code 
Randomly permute a sequence, or return a permuted range.

Parameters
----------
x : int or array_like
    If `x` is an integer, randomly permute ``np.arange(x)``.
    If `x` is an array, make a copy and shuffle the elements
    randomly.

Returns
-------
out : ndarray
    Permuted sequence or array range.

Examples
--------
>>> np.random.permutation(10)
array([1, 7, 4, 3, 0, 9, 2, 5, 8, 6])

>>> np.random.permutation([1, 4, 9, 12, 15])
array([15,  1,  9,  4, 12])

rand(d0, d1, dn, ...)

source code 
Random values in a given shape.

Create an array of the given shape and propagate it with
random samples from a uniform distribution
over ``[0, 1)``.

Parameters
----------
d0, d1, ..., dn : int
    Shape of the output.

Returns
-------
out : ndarray, shape ``(d0, d1, ..., dn)``
    Random values.

See Also
--------
random

Notes
-----
This is a convenience function. If you want an interface that
takes a shape-tuple as the first argument, refer to
`random`.

Examples
--------
>>> np.random.rand(3,2)
array([[ 0.14022471,  0.96360618],  #random
       [ 0.37601032,  0.25528411],  #random
       [ 0.49313049,  0.94909878]]) #random

randint(low, high=None, size=None)

source code 

Return random integers x such that low <= x < high.

If high is None, then 0 <= x < low.

randn(d0, d1, dn, ...)

source code 
Returns zero-mean, unit-variance Gaussian random numbers in an
array of shape (d0, d1, ..., dn).

Note:  This is a convenience function. If you want an
            interface that takes a tuple as the first argument
            use numpy.random.standard_normal(shape_tuple).

random_integers(low, high=None, size=None)

source code 

Return random integers x such that low <= x <= high.

If high is None, then 1 <= x <= low.

random_sample(size=None)

source code 
Return random floats in the half-open interval [0.0, 1.0).

Parameters
----------
size : shape tuple, optional
    Defines the shape of the returned array of random floats.

Returns
-------
out : ndarray, floats
    Array of random of floats with shape of `size`.

seed(seed=None)

source code 

Seed the generator.

seed can be an integer, an array (or other sequence) of integers of any length, or None. If seed is None, then RandomState will try to read data from /dev/urandom (or the Windows analogue) if available or seed from the clock otherwise.

set_state(state)

source code 
Set the state from a tuple.

Parameters
----------
state : tuple(string, list of 624 ints, int, int, float)
    The `state` tuple is made up of

    1. the string 'MT19937'
    2. a list of 624 integer keys
    3. an integer pos
    4. an integer has_gauss
    5. and a float for the cached_gaussian

Returns
-------
out : None
    Returns 'None' on success.

See Also
--------
get_state

Notes
-----
For backwards compatibility, the following form is also accepted
although it is missing some information about the cached Gaussian value.

state = ('MT19937', int key[624], int pos)

standard_normal(size=None)

source code 
Returns samples from a Standard Normal distribution (mean=0, stdev=1).

Parameters
----------
size : int, shape tuple, optional
    Returns the number of samples required to satisfy the `size` parameter.
    If not given or 'None' indicates to return one sample.

Returns
-------
out : float, ndarray
    Samples the Standard Normal distribution with a shape satisfying the
    `size` parameter.

uniform(low=0.0, high=1.0, size=1)

source code 
Draw samples from a uniform distribution.

Samples are uniformly distributed over the half-open interval
``[low, high)`` (includes low, but excludes high).  In other words,
any value within the given interval is equally likely to be drawn
by `uniform`.

Parameters
----------
low : float, optional
    Lower boundary of the output interval.  All values generated will be
    greater than or equal to low.  The default value is 0.
high : float
    Upper boundary of the output interval.  All values generated will be
    less than high.  The default value is 1.0.
size : tuple of ints, int, optional
    Shape of output.  If the given size is, for example, (m,n,k),
    m*n*k samples are generated.  If no shape is specified, a single sample
    is returned.

Returns
-------
out : ndarray
    Drawn samples, with shape `size`.

See Also
--------
randint : Discrete uniform distribution, yielding integers.
random_integers : Discrete uniform distribution over the closed interval
                  ``[low, high]``.
random_sample : Floats uniformly distributed over ``[0, 1)``.
random : Alias for `random_sample`.
rand : Convenience function that accepts dimensions as input, e.g.,
       ``rand(2,2)`` would generate a 2-by-2 array of floats, uniformly
       distributed over ``[0, 1)``.

Notes
-----
The probability density function of the uniform distribution is

.. math:: p(x) = \frac{1}{b - a}

anywhere within the interval ``[a, b)``, and zero elsewhere.

Examples
--------
Draw samples from the distribution:

>>> s = np.random.uniform(-1,0,1000)

All values are within the given interval:

>>> np.all(s >= -1)
True

>>> np.all(s < 0)
True

Display the histogram of the samples, along with the
probability density function:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 15, normed=True)
>>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')
>>> plt.show()

vonmises(mu=0.0, kappa=1.0, size=None)

source code 
Draw samples from a von Mises distribution.

Samples are drawn from a von Mises distribution with specified mode (mu)
and dispersion (kappa), on the interval [-pi, pi].

The von Mises distribution (also known as the circular normal
distribution) is a continuous probability distribution on the circle. It
may be thought of as the circular analogue of the normal distribution.

Parameters
----------
mu : float
    Mode ("center") of the distribution.
kappa : float, >= 0.
    Dispersion of the distribution.
size : {tuple, int}
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
samples : {ndarray, scalar}
    The returned samples live on the unit circle [-\pi, \pi].

See Also
--------
scipy.stats.distributions.vonmises : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the von Mises distribution is

.. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)},

where :math:`\mu` is the mode and :math:`\kappa` the dispersion,
and :math:`I_0(\kappa)` is the modified Bessel function of order 0.

The von Mises, named for Richard Edler von Mises, born in
Austria-Hungary, in what is now the Ukraine. He fled to the United
States in 1939 and became a professor at Harvard. He worked in
probability theory, aerodynamics, fluid mechanics, and philosophy of
science.

References
----------
.. [1] Abramowitz, M. and Stegun, I. A. (ed.), Handbook of Mathematical
       Functions, National Bureau of Standards, 1964; reprinted Dover
       Publications, 1965.
.. [2] von Mises, Richard, 1964, Mathematical Theory of Probability
       and Statistics (New York: Academic Press).
.. [3] Wikipedia, "Von Mises distribution",
       http://en.wikipedia.org/wiki/Von_Mises_distribution

Examples
--------
Draw samples from the distribution:

>>> mu, kappa = 0.0, 4.0 # mean and dispersion
>>> s = np.random.vonmises(mu, kappa, 1000)

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> import scipy.special as sps
>>> count, bins, ignored = plt.hist(s, 50, normed=True)
>>> x = arange(-pi, pi, 2*pi/50.)
>>> y = -np.exp(kappa*np.cos(x-mu))/(2*pi*sps.jn(0,kappa))
>>> plt.plot(x, y/max(y), linewidth=2, color='r')
>>> plt.show()

weibull(a, size=None)

source code 
Weibull distribution.

Draw samples from a 1-parameter Weibull distribution with the given
shape parameter.

.. math:: X = (-ln(U))^{1/a}

Here, U is drawn from the uniform distribution over (0,1].

The more common 2-parameter Weibull, including a scale parameter
:math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`.

The Weibull (or Type III asymptotic extreme value distribution for smallest
values, SEV Type III, or Rosin-Rammler distribution) is one of a class of
Generalized Extreme Value (GEV) distributions used in modeling extreme
value problems.  This class includes the Gumbel and Frechet distributions.

Parameters
----------
a : float
    Shape of the distribution.
size : tuple of ints
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

See Also
--------
scipy.stats.distributions.weibull : probability density function,
    distribution or cumulative density function, etc.

gumbel, scipy.stats.distributions.genextreme

Notes
-----
The probability density for the Weibull distribution is

.. math:: p(x) = \frac{a}
                 {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a},

where :math:`a` is the shape and :math:`\lambda` the scale.

The function has its peak (the mode) at
:math:`\lambda(\frac{a-1}{a})^{1/a}`.

When ``a = 1``, the Weibull distribution reduces to the exponential
distribution.

References
----------
.. [1] Waloddi Weibull, Professor, Royal Technical University, Stockholm,
       1939 "A Statistical Theory Of The Strength Of Materials",
       Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939,
       Generalstabens Litografiska Anstalts Forlag, Stockholm.
.. [2] Waloddi Weibull, 1951 "A Statistical Distribution Function of Wide
       Applicability",  Journal Of Applied Mechanics ASME Paper.
.. [3] Wikipedia, "Weibull distribution",
       http://en.wikipedia.org/wiki/Weibull_distribution

Examples
--------
Draw samples from the distribution:

>>> a = 5. # shape
>>> s = np.random.weibull(a, 1000)

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> def weib(x,n,a):
...     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)

>>> count, bins, ignored = plt.hist(np.random.weibull(5.,1000))
>>> x = np.arange(1,100.)/50.
>>> scale = count.max()/weib(x, 1., 5.).max()
>>> plt.plot(x, weib(x, 1., 5.)*scale)
>>> plt.show()

zipf(a, size=None)

source code 
Draw samples from a Zipf distribution.

Samples are drawn from a Zipf distribution with specified parameter (a),
where a > 1.

The zipf distribution (also known as the zeta
distribution) is a continuous probability distribution that satisfies
Zipf's law, where the frequency of an item is inversely proportional to
its rank in a frequency table.

Parameters
----------
a : float
    parameter, > 1.
size : {tuple, int}
    Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
    ``m * n * k`` samples are drawn.

Returns
-------
samples : {ndarray, scalar}
    The returned samples are greater than or equal to one.

See Also
--------
scipy.stats.distributions.zipf : probability density function,
    distribution or cumulative density function, etc.

Notes
-----
The probability density for the Zipf distribution is

.. math:: p(x) = \frac{x^{-a}}{\zeta(a)},

where :math:`\zeta` is the Riemann Zeta function.

Named after the American linguist George Kingsley Zipf, who noted that
the frequency of any word in a sample of a language is inversely
proportional to its rank in the frequency table.


References
----------
.. [1] Weisstein, Eric W. "Zipf Distribution." From MathWorld--A Wolfram
       Web Resource. http://mathworld.wolfram.com/ZipfDistribution.html
.. [2] Wikipedia, "Zeta distribution",
       http://en.wikipedia.org/wiki/Zeta_distribution
.. [3] Wikipedia, "Zipf's Law",
       http://en.wikipedia.org/wiki/Zipf%27s_law
.. [4] Zipf, George Kingsley (1932): Selected Studies of the Principle
       of Relative Frequency in Language. Cambridge (Mass.).

Examples
--------
Draw samples from the distribution:

>>> a = 2. # parameter
>>> s = np.random.zipf(a, 1000)

Display the histogram of the samples, along with
the probability density function:

>>> import matplotlib.pyplot as plt
>>> import scipy.special as sps
Truncate s values at 50 so plot is interesting
>>> count, bins, ignored = plt.hist(s[s<50], 50, normed=True)
>>> x = arange(1., 50.)
>>> y = x**(-a)/sps.zetac(a)
>>> plt.plot(x, y/max(y), linewidth=2, color='r')
>>> plt.show()


Variables Details [hide private]

ScalarType

Value:
(<type 'int'>,
 <type 'float'>,
 <type 'complex'>,
 <type 'long'>,
 <type 'bool'>,
 <type 'str'>,
 <type 'unicode'>,
 <type 'buffer'>,
...

cast

Value:
{<type 'numpy.int64'>: <function <lambda> at 0xa9a741c>, <type 'numpy.\
int16'>: <function <lambda> at 0xa9a7454>, <type 'numpy.object_'>: <fu\
nction <lambda> at 0xa9a748c>, <type 'numpy.uint32'>: <function <lambd\
a> at 0xa9a74c4>, <type 'numpy.bool_'>: <function <lambda> at 0xa9a74f\
c>, <type 'numpy.float96'>: <function <lambda> at 0xa9a7534>, <type 'n\
umpy.int32'>: <function <lambda> at 0xa9a756c>, <type 'numpy.string_'>\
: <function <lambda> at 0xa9a75a4>, <type 'numpy.uint32'>: <function <\
lambda> at 0xa9a75dc>, <type 'numpy.complex64'>: <function <lambda> at\
...

index_exp

Value:
<numpy.lib.index_tricks.IndexExpression object at 0xaaa83ac>

nbytes

Value:
{<type 'numpy.int64'>: 8, <type 'numpy.int16'>: 2, <type 'numpy.object\
_'>: 4, <type 'numpy.uint32'>: 4, <type 'numpy.bool_'>: 1, <type 'nump\
y.float96'>: 12, <type 'numpy.int32'>: 4, <type 'numpy.string_'>: 0, <\
type 'numpy.uint32'>: 4, <type 'numpy.complex64'>: 8, <type 'numpy.uni\
code_'>: 0, <type 'numpy.uint64'>: 8, <type 'numpy.int8'>: 1, <type 'n\
umpy.complex128'>: 16, <type 'numpy.uint8'>: 1, <type 'numpy.int32'>: \
4, <type 'numpy.void'>: 0, <type 'numpy.float32'>: 4, <type 'numpy.com\
plex192'>: 24, <type 'numpy.uint16'>: 2, <type 'numpy.float64'>: 8}

sctypeDict

Value:
{0: <type 'numpy.bool_'>,
 1: <type 'numpy.int8'>,
 2: <type 'numpy.uint8'>,
 3: <type 'numpy.int16'>,
 4: <type 'numpy.uint16'>,
 5: <type 'numpy.int32'>,
 6: <type 'numpy.uint32'>,
 7: <type 'numpy.int32'>,
...

sctypeNA

Value:
{'?': 'Bool',
 'B': 'UInt8',
 'Bool': <type 'numpy.bool_'>,
 'Complex32': <type 'numpy.complex64'>,
 'Complex64': <type 'numpy.complex128'>,
 'Complex96': <type 'numpy.complex192'>,
 'D': 'Complex64',
 'F': 'Complex32',
...

sctypes

Value:
{'complex': [<type 'numpy.complex64'>,
             <type 'numpy.complex128'>,
             <type 'numpy.complex192'>],
 'float': [<type 'numpy.float32'>,
           <type 'numpy.float64'>,
           <type 'numpy.float96'>],
 'int': [<type 'numpy.int8'>,
         <type 'numpy.int16'>,
...

typeDict

Value:
{0: <type 'numpy.bool_'>,
 1: <type 'numpy.int8'>,
 2: <type 'numpy.uint8'>,
 3: <type 'numpy.int16'>,
 4: <type 'numpy.uint16'>,
 5: <type 'numpy.int32'>,
 6: <type 'numpy.uint32'>,
 7: <type 'numpy.int32'>,
...

typeNA

Value:
{'?': 'Bool',
 'B': 'UInt8',
 'Bool': <type 'numpy.bool_'>,
 'Complex32': <type 'numpy.complex64'>,
 'Complex64': <type 'numpy.complex128'>,
 'Complex96': <type 'numpy.complex192'>,
 'D': 'Complex64',
 'F': 'Complex32',
...

typecodes

Value:
{'All': '?bhilqpBHILQPfdgFDGSUVO',
 'AllFloat': 'fdgFDG',
 'AllInteger': 'bBhHiIlLqQpP',
 'Character': 'c',
 'Complex': 'FDG',
 'Float': 'fdg',
 'Integer': 'bhilqp',
 'UnsignedInteger': 'BHILQP'}