scipy.stats.dlaplace#
- scipy.stats.dlaplace = <scipy.stats._discrete_distns.dlaplace_gen object>[source]#
- A Laplacian discrete random variable. - As an instance of the - rv_discreteclass,- dlaplaceobject 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(a, loc=0, size=1, random_state=None) - Random variates. - pmf(k, a, loc=0) - Probability mass function. - logpmf(k, a, loc=0) - Log of the probability mass function. - cdf(k, a, loc=0) - Cumulative distribution function. - logcdf(k, a, loc=0) - Log of the cumulative distribution function. - sf(k, a, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, a, loc=0) - Log of the survival function. - ppf(q, a, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, a, loc=0) - Inverse survival function (inverse of - sf).- stats(a, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(a, loc=0) - (Differential) entropy of the RV. - expect(func, args=(a,), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(a, loc=0) - Median of the distribution. - mean(a, loc=0) - Mean of the distribution. - var(a, loc=0) - Variance of the distribution. - std(a, loc=0) - Standard deviation of the distribution. - interval(confidence, a, loc=0) - Confidence interval with equal areas around the median. - Notes - The probability mass function for - dlaplaceis:\[f(k) = \tanh(a/2) \exp(-a |k|)\]- for integers \(k\) and \(a > 0\). - dlaplacetakes \(a\) as shape parameter.- The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- dlaplace.pmf(k, a, loc)is identically equivalent to- dlaplace.pmf(k - loc, a).- Examples - >>> import numpy as np >>> from scipy.stats import dlaplace >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> a = 0.8 >>> lb, ub = dlaplace.support(a) - Calculate the first four moments: - >>> mean, var, skew, kurt = dlaplace.stats(a, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(dlaplace.ppf(0.01, a), ... dlaplace.ppf(0.99, a)) >>> ax.plot(x, dlaplace.pmf(x, a), 'bo', ms=8, label='dlaplace pmf') >>> ax.vlines(x, 0, dlaplace.pmf(x, a), colors='b', lw=5, alpha=0.5) - Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed. - Freeze the distribution and display the frozen - pmf:- >>> rv = dlaplace(a) >>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, ... label='frozen pmf') >>> ax.legend(loc='best', frameon=False) >>> plt.show()   - Check accuracy of - cdfand- ppf:- >>> prob = dlaplace.cdf(x, a) >>> np.allclose(x, dlaplace.ppf(prob, a)) True - Generate random numbers: - >>> r = dlaplace.rvs(a, size=1000)