scipy.stats.laplace_asymmetric#
- scipy.stats.laplace_asymmetric = <scipy.stats._continuous_distns.laplace_asymmetric_gen object>[source]#
- An asymmetric Laplace continuous random variable. - As an instance of the - rv_continuousclass,- laplace_asymmetricobject 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 - laplace
- Laplace distribution 
 - Notes - The probability density function for - laplace_asymmetricis\[\begin{split}f(x, \kappa) &= \frac{1}{\kappa+\kappa^{-1}}\exp(-x\kappa),\quad x\ge0\\ &= \frac{1}{\kappa+\kappa^{-1}}\exp(x/\kappa),\quad x<0\\\end{split}\]- for \(-\infty < x < \infty\), \(\kappa > 0\). - laplace_asymmetrictakes- kappaas a shape parameter for \(\kappa\). For \(\kappa = 1\), it is identical to a Laplace distribution.- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- laplace_asymmetric.pdf(x, kappa, loc, scale)is identically equivalent to- laplace_asymmetric.pdf(y, kappa) / 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.- Note that the scale parameter of some references is the reciprocal of SciPy’s - scale. For example, \(\lambda = 1/2\) in the parameterization of [1] is equivalent to- scale = 2with- laplace_asymmetric.- References [1]- “Asymmetric Laplace distribution”, Wikipedia https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution [2]- Kozubowski TJ and Podgórski K. A Multivariate and Asymmetric Generalization of Laplace Distribution, Computational Statistics 15, 531–540 (2000). DOI:10.1007/PL00022717 - Examples - >>> import numpy as np >>> from scipy.stats import laplace_asymmetric >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> kappa = 2 >>> mean, var, skew, kurt = laplace_asymmetric.stats(kappa, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(laplace_asymmetric.ppf(0.01, kappa), ... laplace_asymmetric.ppf(0.99, kappa), 100) >>> ax.plot(x, laplace_asymmetric.pdf(x, kappa), ... 'r-', lw=5, alpha=0.6, label='laplace_asymmetric 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 = laplace_asymmetric(kappa) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = laplace_asymmetric.ppf([0.001, 0.5, 0.999], kappa) >>> np.allclose([0.001, 0.5, 0.999], laplace_asymmetric.cdf(vals, kappa)) True - Generate random numbers: - >>> r = laplace_asymmetric.rvs(kappa, 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(kappa, loc=0, scale=1, size=1, random_state=None) - Random variates. - pdf(x, kappa, loc=0, scale=1) - Probability density function. - logpdf(x, kappa, loc=0, scale=1) - Log of the probability density function. - cdf(x, kappa, loc=0, scale=1) - Cumulative distribution function. - logcdf(x, kappa, loc=0, scale=1) - Log of the cumulative distribution function. - sf(x, kappa, loc=0, scale=1) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(x, kappa, loc=0, scale=1) - Log of the survival function. - ppf(q, kappa, loc=0, scale=1) - Percent point function (inverse of - cdf— percentiles).- isf(q, kappa, loc=0, scale=1) - Inverse survival function (inverse of - sf).- moment(order, kappa, loc=0, scale=1) - Non-central moment of the specified order. - stats(kappa, loc=0, scale=1, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(kappa, 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=(kappa,), 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(kappa, loc=0, scale=1) - Median of the distribution. - mean(kappa, loc=0, scale=1) - Mean of the distribution. - var(kappa, loc=0, scale=1) - Variance of the distribution. - std(kappa, loc=0, scale=1) - Standard deviation of the distribution. - interval(confidence, kappa, loc=0, scale=1) - Confidence interval with equal areas around the median.