scipy.stats.genexpon#
- scipy.stats.genexpon = <scipy.stats._continuous_distns.genexpon_gen object>[source]#
- A generalized exponential continuous random variable. - As an instance of the - rv_continuousclass,- genexponobject 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 - genexponis:\[f(x, a, b, c) = (a + b (1 - \exp(-c x))) \exp(-a x - b x + \frac{b}{c} (1-\exp(-c x)))\]- for \(x \ge 0\), \(a, b, c > 0\). - genexpontakes \(a\), \(b\) and \(c\) as shape parameters.- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- genexpon.pdf(x, a, b, c, loc, scale)is identically equivalent to- genexpon.pdf(y, a, b, c) / scalewith- y = (x - loc) / scale. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes.- References - H.K. Ryu, “An Extension of Marshall and Olkin’s Bivariate Exponential Distribution”, Journal of the American Statistical Association, 1993. - N. Balakrishnan, Asit P. Basu (editors), The Exponential Distribution: Theory, Methods and Applications, Gordon and Breach, 1995. ISBN 10: 2884491929 - Examples - >>> import numpy as np >>> from scipy.stats import genexpon >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> a, b, c = 9.13, 16.2, 3.28 >>> mean, var, skew, kurt = genexpon.stats(a, b, c, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(genexpon.ppf(0.01, a, b, c), ... genexpon.ppf(0.99, a, b, c), 100) >>> ax.plot(x, genexpon.pdf(x, a, b, c), ... 'r-', lw=5, alpha=0.6, label='genexpon 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 = genexpon(a, b, c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = genexpon.ppf([0.001, 0.5, 0.999], a, b, c) >>> np.allclose([0.001, 0.5, 0.999], genexpon.cdf(vals, a, b, c)) True - Generate random numbers: - >>> r = genexpon.rvs(a, b, c, 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()   - Methods - rvs(a, b, c, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, a, b, c, loc=0, scale=1) - Probability density function. - logpdf(x, a, b, c, loc=0, scale=1) - Log of the probability density function. - cdf(x, a, b, c, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, a, b, c, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, a, b, c, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, a, b, c, loc=0, scale=1) - Log of the survival function. - ppf(q, a, b, c, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, a, b, c, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, a, b, c, loc=0, scale=1) - Non-central moment of the specified order. - stats(a, b, c, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(a, b, c, 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=(a, b, c), 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(a, b, c, loc=0, scale=1) - Median of the distribution. - mean(a, b, c, loc=0, scale=1) - Mean of the distribution. - var(a, b, c, loc=0, scale=1) - Variance of the distribution. - std(a, b, c, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, a, b, c, loc=0, scale=1) - Confidence interval with equal areas around the median.