scipy.stats.halfgennorm¶
- scipy.stats.halfgennorm = <scipy.stats._continuous_distns.halfgennorm_gen object at 0x2b2318ee6ad0>[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
Notes
The probability density function for halfgennorm is:
beta halfgennorm.pdf(x, beta) = ------------- exp(-|x|**beta) gamma(1/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
[R588] “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()
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