scipy.stats.genpareto#
- scipy.stats.genpareto = <scipy.stats._continuous_distns.genpareto_gen object>[source]#
- A generalized Pareto continuous random variable. - As an instance of the - rv_continuousclass,- genparetoobject 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 - genparetois:\[f(x, c) = (1 + c x)^{-1 - 1/c}\]- defined for \(x \ge 0\) if \(c \ge 0\), and for \(0 \le x \le -1/c\) if \(c < 0\). - genparetotakes- cas a shape parameter for \(c\).- For \(c=0\), - genparetoreduces to the exponential distribution,- expon:\[f(x, 0) = \exp(-x)\]- For \(c=-1\), - genparetois uniform on- [0, 1]:\[f(x, -1) = 1\]- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- genpareto.pdf(x, c, loc, scale)is identically equivalent to- genpareto.pdf(y, 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.- Examples - >>> import numpy as np >>> from scipy.stats import genpareto >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> c = 0.1 >>> mean, var, skew, kurt = genpareto.stats(c, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(genpareto.ppf(0.01, c), ... genpareto.ppf(0.99, c), 100) >>> ax.plot(x, genpareto.pdf(x, c), ... 'r-', lw=5, alpha=0.6, label='genpareto 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 = genpareto(c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = genpareto.ppf([0.001, 0.5, 0.999], c) >>> np.allclose([0.001, 0.5, 0.999], genpareto.cdf(vals, c)) True - Generate random numbers: - >>> r = genpareto.rvs(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(c, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, c, loc=0, scale=1) - Probability density function. - logpdf(x, c, loc=0, scale=1) - Log of the probability density function. - cdf(x, c, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, c, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, c, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, c, loc=0, scale=1) - Log of the survival function. - ppf(q, c, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, c, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, c, loc=0, scale=1) - Non-central moment of the specified order. - stats(c, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(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=(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(c, loc=0, scale=1) - Median of the distribution. - mean(c, loc=0, scale=1) - Mean of the distribution. - var(c, loc=0, scale=1) - Variance of the distribution. - std(c, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, c, loc=0, scale=1) - Confidence interval with equal areas around the median.