aub_htp.alpha_stable#

aub_htp.alpha_stable = <aub_htp._alpha_stable.alpha_stable_gen object>#

A Distribution continuous random variable.

As an instance of the rv_continuous class, Distribution 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(alpha, beta, loc=0, scale=1, size=1, random_state=None)

Random variates.

pdf(x, alpha, beta, loc=0, scale=1)

Probability density function.

logpdf(x, alpha, beta, loc=0, scale=1)

Log of the probability density function.

cdf(x, alpha, beta, loc=0, scale=1)

Cumulative distribution function.

logcdf(x, alpha, beta, loc=0, scale=1)

Log of the cumulative distribution function.

sf(x, alpha, beta, loc=0, scale=1)

Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).

logsf(x, alpha, beta, loc=0, scale=1)

Log of the survival function.

ppf(q, alpha, beta, loc=0, scale=1)

Percent point function (inverse of cdf — percentiles).

isf(q, alpha, beta, loc=0, scale=1)

Inverse survival function (inverse of sf).

moment(order, alpha, beta, loc=0, scale=1)

Non-central moment of the specified order.

stats(alpha, beta, loc=0, scale=1, moments=’mv’)

Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).

entropy(alpha, beta, loc=0, scale=1)

(Differential) entropy of the RV.

fit(data)

Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments.

expect(func, args=(alpha, beta), 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(alpha, beta, loc=0, scale=1)

Median of the distribution.

mean(alpha, beta, loc=0, scale=1)

Mean of the distribution.

var(alpha, beta, loc=0, scale=1)

Variance of the distribution.

std(alpha, beta, loc=0, scale=1)

Standard deviation of the distribution.

interval(confidence, alpha, beta, loc=0, scale=1)

Confidence interval with equal areas around the median.

Notes#

Examples#

>>> import numpy as np
>>> from scipy.stats import Distribution
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Get the support:

>>> alpha, beta = 
>>> lb, ub = Distribution.support(alpha, beta)

Calculate the first four moments:

>>> mean, var, skew, kurt = Distribution.stats(alpha, beta, moments='mvsk')

Display the probability density function (pdf):

>>> x = np.linspace(Distribution.ppf(0.01, alpha, beta),
...                 Distribution.ppf(0.99, alpha, beta), 100)
>>> ax.plot(x, Distribution.pdf(x, alpha, beta),
...        'r-', lw=5, alpha=0.6, label='Distribution 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 = Distribution(alpha, beta)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

>>> vals = Distribution.ppf([0.001, 0.5, 0.999], alpha, beta)
>>> np.allclose([0.001, 0.5, 0.999], Distribution.cdf(vals, alpha, beta))
True

Generate random numbers:

>>> r = Distribution.rvs(alpha, beta, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
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