scipy sp1.4-0.3.0 · OCaml Package

val get_py : string -> Py.Object.t

Get an attribute of this module as a Py.Object.t. This is useful to pass a Python function to another function.

module Alpha_gen : sig ... end

module Anglit_gen : sig ... end

module Arcsine_gen : sig ... end

module Argus_gen : sig ... end

module Bernoulli_gen : sig ... end

module Beta_gen : sig ... end

module Betabinom_gen : sig ... end

module Betaprime_gen : sig ... end

module Binom_gen : sig ... end

module Boltzmann_gen : sig ... end

module Bradford_gen : sig ... end

module Burr12_gen : sig ... end

module Burr_gen : sig ... end

module Cauchy_gen : sig ... end

module Chi2_gen : sig ... end

module Chi_gen : sig ... end

module Cosine_gen : sig ... end

module Crystalball_gen : sig ... end

module Dgamma_gen : sig ... end

module Dlaplace_gen : sig ... end

module Dweibull_gen : sig ... end

module Erlang_gen : sig ... end

module Expon_gen : sig ... end

module Exponnorm_gen : sig ... end

module Exponpow_gen : sig ... end

module Exponweib_gen : sig ... end

module F_gen : sig ... end

module Fatiguelife_gen : sig ... end

module Fisk_gen : sig ... end

module Foldcauchy_gen : sig ... end

module Foldnorm_gen : sig ... end

module Frechet_l_gen : sig ... end

module Frechet_r_gen : sig ... end

module Gamma_gen : sig ... end

module Gausshyper_gen : sig ... end

module Genexpon_gen : sig ... end

module Genextreme_gen : sig ... end

module Gengamma_gen : sig ... end

module Genhalflogistic_gen : sig ... end

module Geninvgauss_gen : sig ... end

module Genlogistic_gen : sig ... end

module Gennorm_gen : sig ... end

module Genpareto_gen : sig ... end

module Geom_gen : sig ... end

module Gilbrat_gen : sig ... end

module Gompertz_gen : sig ... end

module Gumbel_l_gen : sig ... end

module Gumbel_r_gen : sig ... end

module Halfcauchy_gen : sig ... end

module Halfgennorm_gen : sig ... end

module Halflogistic_gen : sig ... end

module Halfnorm_gen : sig ... end

module Hypergeom_gen : sig ... end

module Hypsecant_gen : sig ... end

module Invgamma_gen : sig ... end

module Invgauss_gen : sig ... end

module Invweibull_gen : sig ... end

module Johnsonsb_gen : sig ... end

module Johnsonsu_gen : sig ... end

module Kappa3_gen : sig ... end

module Kappa4_gen : sig ... end

module Ksone_gen : sig ... end

module Kstwobign_gen : sig ... end

module Laplace_gen : sig ... end

module Levy_gen : sig ... end

module Levy_l_gen : sig ... end

module Levy_stable_gen : sig ... end

module Loggamma_gen : sig ... end

module Logistic_gen : sig ... end

module Loglaplace_gen : sig ... end

module Lognorm_gen : sig ... end

module Logser_gen : sig ... end

module Lomax_gen : sig ... end

module Maxwell_gen : sig ... end

module Mielke_gen : sig ... end

module Moyal_gen : sig ... end

module Nakagami_gen : sig ... end

module Nbinom_gen : sig ... end

module Ncf_gen : sig ... end

module Nct_gen : sig ... end

module Ncx2_gen : sig ... end

module Norm_gen : sig ... end

module Norminvgauss_gen : sig ... end

module Pareto_gen : sig ... end

module Pearson3_gen : sig ... end

module Planck_gen : sig ... end

module Poisson_gen : sig ... end

module Powerlaw_gen : sig ... end

module Powerlognorm_gen : sig ... end

module Powernorm_gen : sig ... end

module Randint_gen : sig ... end

module Rayleigh_gen : sig ... end

module Rdist_gen : sig ... end

module Recipinvgauss_gen : sig ... end

module Reciprocal_gen : sig ... end

module Rice_gen : sig ... end

module Rv_frozen : sig ... end

module Semicircular_gen : sig ... end

module Skellam_gen : sig ... end

module Skew_norm_gen : sig ... end

module T_gen : sig ... end

module Trapz_gen : sig ... end

module Triang_gen : sig ... end

module Truncexpon_gen : sig ... end

module Truncnorm_gen : sig ... end

module Tukeylambda_gen : sig ... end

module Uniform_gen : sig ... end

module Vonmises_gen : sig ... end

module Wald_gen : sig ... end

module Weibull_max_gen : sig ... end

module Weibull_min_gen : sig ... end

module Wrapcauchy_gen : sig ... end

module Yulesimon_gen : sig ... end

module Zipf_gen : sig ... end

val alpha : 
  ?loc:float ->
  ?scale:float ->
  a:Py.Object.t ->
  unit ->
  [ `Alpha_gen | `Object | `Rv_continuous | `Rv_generic ] Np.Obj.t

An alpha continuous random variable.

As an instance of the `rv_continuous` class, `alpha` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(a, loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, a, loc=0, scale=1) Probability density function. logpdf(x, a, loc=0, scale=1) Log of the probability density function. cdf(x, a, loc=0, scale=1) Cumulative distribution function. logcdf(x, a, loc=0, scale=1) Log of the cumulative distribution function. sf(x, a, loc=0, scale=1) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(x, a, loc=0, scale=1) Log of the survival function. ppf(q, a, loc=0, scale=1) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, a, loc=0, scale=1) Inverse survival function (inverse of ``sf``). moment(n, a, loc=0, scale=1) Non-central moment of order n stats(a, loc=0, scale=1, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(a, loc=0, scale=1) (Differential) entropy of the RV. fit(data, a, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(a,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) Expected value of a function (of one argument) with respect to the distribution. median(a, loc=0, scale=1) Median of the distribution. mean(a, loc=0, scale=1) Mean of the distribution. var(a, loc=0, scale=1) Variance of the distribution. std(a, loc=0, scale=1) Standard deviation of the distribution. interval(alpha, a, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The probability density function for `alpha` (1_, 2_) is:

.. math::

f(x, a) = \frac

x^2 \Phi(a) \sqrt{2\pi

}

* \exp(-\frac

(a-1/x)^2)

where :math:`\Phi` is the normal CDF, :math:`x > 0`, and :math:`a > 0`.

`alpha` takes ``a`` as a shape parameter.

The probability density above is defined in the 'standardized' form. To shift and/or scale the distribution use the ``loc`` and ``scale`` parameters. Specifically, ``alpha.pdf(x, a, loc, scale)`` is identically equivalent to ``alpha.pdf(y, a) / scale`` with ``y = (x - loc) / scale``.

References ---------- .. 1 Johnson, Kotz, and Balakrishnan, 'Continuous Univariate Distributions, Volume 1', Second Edition, John Wiley and Sons, p. 173 (1994). .. 2 Anthony A. Salvia, 'Reliability applications of the Alpha Distribution', IEEE Transactions on Reliability, Vol. R-34, No. 3, pp. 251-252 (1985).

Examples -------- >>> from scipy.stats import alpha >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> a = 3.57 >>> mean, var, skew, kurt = alpha.stats(a, moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(alpha.ppf(0.01, a), ... alpha.ppf(0.99, a), 100) >>> ax.plot(x, alpha.pdf(x, a), ... 'r-', lw=5, alpha=0.6, label='alpha pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a 'frozen' RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = alpha(a) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = alpha.ppf(0.001, 0.5, 0.999, a) >>> np.allclose(0.001, 0.5, 0.999, alpha.cdf(vals, a)) True

Generate random numbers:

>>> r = alpha.rvs(a, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()

val anglit : 
  ?loc:float ->
  ?scale:float ->
  unit ->
  [ `Anglit_gen | `Object | `Rv_continuous | `Rv_generic ] Np.Obj.t

An anglit continuous random variable.

As an instance of the `rv_continuous` class, `anglit` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, loc=0, scale=1) Probability density function. logpdf(x, loc=0, scale=1) Log of the probability density function. cdf(x, loc=0, scale=1) Cumulative distribution function. logcdf(x, loc=0, scale=1) Log of the cumulative distribution function. sf(x, loc=0, scale=1) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(x, loc=0, scale=1) Log of the survival function. ppf(q, loc=0, scale=1) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, loc=0, scale=1) Inverse survival function (inverse of ``sf``). moment(n, loc=0, scale=1) Non-central moment of order n stats(loc=0, scale=1, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(loc=0, scale=1) (Differential) entropy of the RV. fit(data, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) Expected value of a function (of one argument) with respect to the distribution. median(loc=0, scale=1) Median of the distribution. mean(loc=0, scale=1) Mean of the distribution. var(loc=0, scale=1) Variance of the distribution. std(loc=0, scale=1) Standard deviation of the distribution. interval(alpha, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The probability density function for `anglit` is:

.. math::

f(x) = \sin(2x + \pi/2) = \cos(2x)

for :math:`-\pi/4 \le x \le \pi/4`.

The probability density above is defined in the 'standardized' form. To shift and/or scale the distribution use the ``loc`` and ``scale`` parameters. Specifically, ``anglit.pdf(x, loc, scale)`` is identically equivalent to ``anglit.pdf(y) / scale`` with ``y = (x - loc) / scale``.

Examples -------- >>> from scipy.stats import anglit >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> mean, var, skew, kurt = anglit.stats(moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(anglit.ppf(0.01), ... anglit.ppf(0.99), 100) >>> ax.plot(x, anglit.pdf(x), ... 'r-', lw=5, alpha=0.6, label='anglit pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a 'frozen' RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = anglit() >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = anglit.ppf(0.001, 0.5, 0.999) >>> np.allclose(0.001, 0.5, 0.999, anglit.cdf(vals)) True

Generate random numbers:

>>> r = anglit.rvs(size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()

val arcsine : 
  ?loc:float ->
  ?scale:float ->
  unit ->
  [ `Arcsine_gen | `Object | `Rv_continuous | `Rv_generic ] Np.Obj.t

An arcsine continuous random variable.

As an instance of the `rv_continuous` class, `arcsine` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, loc=0, scale=1) Probability density function. logpdf(x, loc=0, scale=1) Log of the probability density function. cdf(x, loc=0, scale=1) Cumulative distribution function. logcdf(x, loc=0, scale=1) Log of the cumulative distribution function. sf(x, loc=0, scale=1) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(x, loc=0, scale=1) Log of the survival function. ppf(q, loc=0, scale=1) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, loc=0, scale=1) Inverse survival function (inverse of ``sf``). moment(n, loc=0, scale=1) Non-central moment of order n stats(loc=0, scale=1, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(loc=0, scale=1) (Differential) entropy of the RV. fit(data, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) Expected value of a function (of one argument) with respect to the distribution. median(loc=0, scale=1) Median of the distribution. mean(loc=0, scale=1) Mean of the distribution. var(loc=0, scale=1) Variance of the distribution. std(loc=0, scale=1) Standard deviation of the distribution. interval(alpha, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The probability density function for `arcsine` is:

.. math::

f(x) = \frac

\pi \sqrt{x (1-x)

}

for :math:`0 < x < 1`.

The probability density above is defined in the 'standardized' form. To shift and/or scale the distribution use the ``loc`` and ``scale`` parameters. Specifically, ``arcsine.pdf(x, loc, scale)`` is identically equivalent to ``arcsine.pdf(y) / scale`` with ``y = (x - loc) / scale``.

Examples -------- >>> from scipy.stats import arcsine >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> mean, var, skew, kurt = arcsine.stats(moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(arcsine.ppf(0.01), ... arcsine.ppf(0.99), 100) >>> ax.plot(x, arcsine.pdf(x), ... 'r-', lw=5, alpha=0.6, label='arcsine pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a 'frozen' RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = arcsine() >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = arcsine.ppf(0.001, 0.5, 0.999) >>> np.allclose(0.001, 0.5, 0.999, arcsine.cdf(vals)) True

Generate random numbers:

>>> r = arcsine.rvs(size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()

val argus : 
  ?loc:float ->
  ?scale:float ->
  chi:Py.Object.t ->
  unit ->
  [ `Argus_gen | `Object | `Rv_continuous | `Rv_generic ] Np.Obj.t

Argus distribution

As an instance of the `rv_continuous` class, `argus` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(chi, loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, chi, loc=0, scale=1) Probability density function. logpdf(x, chi, loc=0, scale=1) Log of the probability density function. cdf(x, chi, loc=0, scale=1) Cumulative distribution function. logcdf(x, chi, loc=0, scale=1) Log of the cumulative distribution function. sf(x, chi, loc=0, scale=1) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(x, chi, loc=0, scale=1) Log of the survival function. ppf(q, chi, loc=0, scale=1) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, chi, loc=0, scale=1) Inverse survival function (inverse of ``sf``). moment(n, chi, loc=0, scale=1) Non-central moment of order n stats(chi, loc=0, scale=1, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(chi, loc=0, scale=1) (Differential) entropy of the RV. fit(data, chi, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(chi,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) Expected value of a function (of one argument) with respect to the distribution. median(chi, loc=0, scale=1) Median of the distribution. mean(chi, loc=0, scale=1) Mean of the distribution. var(chi, loc=0, scale=1) Variance of the distribution. std(chi, loc=0, scale=1) Standard deviation of the distribution. interval(alpha, chi, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The probability density function for `argus` is:

.. math::

f(x, \chi) = \frac\chi^3\sqrt{2\pi \Psi(\chi)

}

x \sqrt

-x^2

\exp(-\chi^2 (1 - x^2)/2)

for :math:`0 < x < 1`, where

.. math::

\Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2

with :math:`\Phi` and :math:`\phi` being the CDF and PDF of a standard normal distribution, respectively.

`argus` takes :math:`\chi` as shape a parameter.

References ----------

.. 1 'ARGUS distribution', https://en.wikipedia.org/wiki/ARGUS_distribution

The probability density above is defined in the 'standardized' form. To shift and/or scale the distribution use the ``loc`` and ``scale`` parameters. Specifically, ``argus.pdf(x, chi, loc, scale)`` is identically equivalent to ``argus.pdf(y, chi) / scale`` with ``y = (x - loc) / scale``.

.. versionadded:: 0.19.0

Examples -------- >>> from scipy.stats import argus >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> chi = 1 >>> mean, var, skew, kurt = argus.stats(chi, moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(argus.ppf(0.01, chi), ... argus.ppf(0.99, chi), 100) >>> ax.plot(x, argus.pdf(x, chi), ... 'r-', lw=5, alpha=0.6, label='argus pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a 'frozen' RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = argus(chi) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = argus.ppf(0.001, 0.5, 0.999, chi) >>> np.allclose(0.001, 0.5, 0.999, argus.cdf(vals, chi)) True

Generate random numbers:

>>> r = argus.rvs(chi, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()

val bernoulli : 
  ?loc:float ->
  p:Py.Object.t ->
  unit ->
  [ `Bernoulli_gen | `Object | `Rv_discrete | `Rv_generic ] Np.Obj.t

A Bernoulli discrete random variable.

As an instance of the `rv_discrete` class, `bernoulli` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(p, loc=0, size=1, random_state=None) Random variates. pmf(k, p, loc=0) Probability mass function. logpmf(k, p, loc=0) Log of the probability mass function. cdf(k, p, loc=0) Cumulative distribution function. logcdf(k, p, loc=0) Log of the cumulative distribution function. sf(k, p, loc=0) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(k, p, loc=0) Log of the survival function. ppf(q, p, loc=0) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, p, loc=0) Inverse survival function (inverse of ``sf``). stats(p, loc=0, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(p, loc=0) (Differential) entropy of the RV. expect(func, args=(p,), loc=0, lb=None, ub=None, conditional=False) Expected value of a function (of one argument) with respect to the distribution. median(p, loc=0) Median of the distribution. mean(p, loc=0) Mean of the distribution. var(p, loc=0) Variance of the distribution. std(p, loc=0) Standard deviation of the distribution. interval(alpha, p, loc=0) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The probability mass function for `bernoulli` is:

.. math::

f(k) = \begincases1-p &\textf k = 0\\ p &\textf k = 1\endcases

for :math:`k` in :math:`{0, 1}`.

`bernoulli` takes :math:`p` as shape parameter.

The probability mass function above is defined in the 'standardized' form. To shift distribution use the ``loc`` parameter. Specifically, ``bernoulli.pmf(k, p, loc)`` is identically equivalent to ``bernoulli.pmf(k - loc, p)``.

Examples -------- >>> from scipy.stats import bernoulli >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> p = 0.3 >>> mean, var, skew, kurt = bernoulli.stats(p, moments='mvsk')

Display the probability mass function (``pmf``):

>>> x = np.arange(bernoulli.ppf(0.01, p), ... bernoulli.ppf(0.99, p)) >>> ax.plot(x, bernoulli.pmf(x, p), 'bo', ms=8, label='bernoulli pmf') >>> ax.vlines(x, 0, bernoulli.pmf(x, p), colors='b', lw=5, alpha=0.5)

Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a 'frozen' RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pmf``:

>>> rv = bernoulli(p) >>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, ... label='frozen pmf') >>> ax.legend(loc='best', frameon=False) >>> plt.show()

Check accuracy of ``cdf`` and ``ppf``:

>>> prob = bernoulli.cdf(x, p) >>> np.allclose(x, bernoulli.ppf(prob, p)) True

Generate random numbers:

>>> r = bernoulli.rvs(p, size=1000)

val beta : 
  ?loc:float ->
  ?scale:float ->
  a:Py.Object.t ->
  b:Py.Object.t ->
  unit ->
  [ `Beta_gen | `Object | `Rv_continuous | `Rv_generic ] Np.Obj.t

A beta continuous random variable.

As an instance of the `rv_continuous` class, `beta` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(a, b, loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, a, b, loc=0, scale=1) Probability density function. logpdf(x, a, b, loc=0, scale=1) Log of the probability density function. cdf(x, a, b, loc=0, scale=1) Cumulative distribution function. logcdf(x, a, b, loc=0, scale=1) Log of the cumulative distribution function. sf(x, a, b, loc=0, scale=1) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(x, a, b, loc=0, scale=1) Log of the survival function. ppf(q, a, b, loc=0, scale=1) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, a, b, loc=0, scale=1) Inverse survival function (inverse of ``sf``). moment(n, a, b, loc=0, scale=1) Non-central moment of order n stats(a, b, loc=0, scale=1, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(a, b, loc=0, scale=1) (Differential) entropy of the RV. fit(data, a, b, loc=0, scale=1) Parameter estimates for generic data. expect(func, args=(a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) Expected value of a function (of one argument) with respect to the distribution. median(a, b, loc=0, scale=1) Median of the distribution. mean(a, b, loc=0, scale=1) Mean of the distribution. var(a, b, loc=0, scale=1) Variance of the distribution. std(a, b, loc=0, scale=1) Standard deviation of the distribution. interval(alpha, a, b, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The probability density function for `beta` is:

.. math::

f(x, a, b) = \frac\Gamma(a+b) x^{a-1 (1-x)^-1

}

\Gamma(a) \Gamma(b)

for :math:`0 <= x <= 1`, :math:`a > 0`, :math:`b > 0`, where :math:`\Gamma` is the gamma function (`scipy.special.gamma`).

`beta` takes :math:`a` and :math:`b` as shape parameters.

The probability density above is defined in the 'standardized' form. To shift and/or scale the distribution use the ``loc`` and ``scale`` parameters. Specifically, ``beta.pdf(x, a, b, loc, scale)`` is identically equivalent to ``beta.pdf(y, a, b) / scale`` with ``y = (x - loc) / scale``.

Examples -------- >>> from scipy.stats import beta >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)

Calculate a few first moments:

>>> a, b = 2.31, 0.627 >>> mean, var, skew, kurt = beta.stats(a, b, moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(beta.ppf(0.01, a, b), ... beta.ppf(0.99, a, b), 100) >>> ax.plot(x, beta.pdf(x, a, b), ... 'r-', lw=5, alpha=0.6, label='beta pdf')

Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a 'frozen' RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = beta(a, b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = beta.ppf(0.001, 0.5, 0.999, a, b) >>> np.allclose(0.001, 0.5, 0.999, beta.cdf(vals, a, b)) True

Generate random numbers:

>>> r = beta.rvs(a, b, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2) >>> ax.legend(loc='best', frameon=False) >>> plt.show()

val betabinom : 
  ?loc:float ->
  n:Py.Object.t ->
  a:Py.Object.t ->
  b:Py.Object.t ->
  unit ->
  [ `Betabinom_gen | `Object | `Rv_discrete | `Rv_generic ] Np.Obj.t

A beta-binomial discrete random variable.

As an instance of the `rv_discrete` class, `betabinom` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Methods ------- rvs(n, a, b, loc=0, size=1, random_state=None) Random variates. pmf(k, n, a, b, loc=0) Probability mass function. logpmf(k, n, a, b, loc=0) Log of the probability mass function. cdf(k, n, a, b, loc=0) Cumulative distribution function. logcdf(k, n, a, b, loc=0) Log of the cumulative distribution function. sf(k, n, a, b, loc=0) Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate). logsf(k, n, a, b, loc=0) Log of the survival function. ppf(q, n, a, b, loc=0) Percent point function (inverse of ``cdf`` --- percentiles). isf(q, n, a, b, loc=0) Inverse survival function (inverse of ``sf``). stats(n, a, b, loc=0, moments='mv') Mean('m'), variance('v'), skew('s'), and/or kurtosis('k'). entropy(n, a, b, loc=0) (Differential) entropy of the RV. expect(func, args=(n, a, b), loc=0, lb=None, ub=None, conditional=False) Expected value of a function (of one argument) with respect to the distribution. median(n, a, b, loc=0) Median of the distribution. mean(n, a, b, loc=0) Mean of the distribution. var(n, a, b, loc=0) Variance of the distribution. std(n, a, b, loc=0) Standard deviation of the distribution. interval(alpha, n, a, b, loc=0) Endpoints of the range that contains alpha percent of the distribution

Notes ----- The beta-binomial distribution is a binomial distribution with a probability of success `p` that follows a beta distribution.

The probability mass function for `betabinom` is:

.. math::

f(k) = \binomnk \fracB(k + a, n - k + b)B(a, b)

for ``k`` in ``

, 1,..., n

``, :math:`n \geq 0`, :math:`a > 0`, :math:`b > 0`, where :math:`B(a, b)` is the beta function.

`betabinom` takes :math:`n`, :math:`a`, and :math:`b` as shape parameters.

References ---------- .. 1 https://en.wikipedia.org/wiki/Beta-binomial_distribution

The probability mass function above is defined in the 'standardized' form. To shift distribution use the ``loc`` parameter. Specifically, ``betabinom.pmf(k, n, a, b, loc)`` is identically equivalent to ``betabinom.pmf(k - loc, n, a, b)``.

.. versionadded:: 1.4.0

package scipy