scipy.stats.halfgennorm¶

scipy.stats.halfgennorm = <scipy.stats._continuous_distns.halfgennorm_gen object>[source]¶

The upper half of a generalized normal continuous random variable.

As an instance of the rv_continuous class, halfgennorm 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.

See also

gennorm: generalized normal distribution
expon: exponential distribution
halfnorm: half normal distribution

Notes

The probability density function for halfgennorm is:

\[f(x, \beta) = \frac{\beta}{\gamma(1/\beta)} \exp(-|x|^\beta)\]

gennorm takes \(\beta\) as a shape parameter. For \(\beta = 1\), it is identical to an exponential distribution. For \(\beta = 2\), it is identical to a half normal distribution (with \(scale=1/\sqrt{2}\)).

References

[R614]

“Generalized normal distribution, Version 1”, https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

Examples

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

Calculate a few first moments:

>>> beta = 0.675
>>> mean, var, skew, kurt = halfgennorm.stats(beta, moments='mvsk')

Display the probability density function (pdf):

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

Check accuracy of cdf and ppf:

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

Generate random numbers:

>>> r = halfgennorm.rvs(beta, size=1000)

And compare the histogram:

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

../_images/scipy-stats-halfgennorm-1.png

Methods

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