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_continuousclass,- halfgennormobject 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(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(order, beta, loc=0, scale=1) - Non-central moment of the specified order. - 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) - Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments. - 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(confidence, beta, loc=0, scale=1) - Confidence interval with equal areas around the median. - See also - Notes - The probability density function for - halfgennormis:\[f(x, \beta) = \frac{\beta}{\Gamma(1/\beta)} \exp(-|x|^\beta)\]- for \(x, \beta > 0\). \(\Gamma\) is the gamma function ( - scipy.special.gamma).- halfgennormtakes- betaas a shape parameter for \(\beta\). 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 [1]- “Generalized normal distribution, Version 1”, https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1 - Examples - >>> import numpy as np >>> from scipy.stats import halfgennorm >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> beta = 0.675 >>> lb, ub = halfgennorm.support(beta) - Calculate the first four moments: - >>> 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 - cdfand- 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, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim([x[0], x[-1]]) >>> ax.legend(loc='best', frameon=False) >>> plt.show() 