SciPy

scipy.stats.argus

scipy.stats.argus(*args, **kwds) = <scipy.stats._continuous_distns.argus_gen object>[source]

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.

Notes

The probability density function for argus is:

\[f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2} \exp(-\chi^2 (1 - x^2)/2)\]

for \(0 < x < 1\) and \(\chi > 0\), where

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

with \(\Phi\) and \(\phi\) being the CDF and PDF of a standard normal distribution, respectively.

argus takes \(\chi\) as shape a 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, argus.pdf(x, chi, loc, scale) is identically equivalent to argus.pdf(y, chi) / scale with y = (x - loc) / scale.

New in version 0.19.0.

References

1

“ARGUS distribution”, https://en.wikipedia.org/wiki/ARGUS_distribution

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()
../_images/scipy-stats-argus-1.png

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)

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

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

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