scipy.stats.loglaplace#
- scipy.stats.loglaplace = <scipy.stats._continuous_distns.loglaplace_gen object>[source]#
- A log-Laplace continuous random variable. - As an instance of the - rv_continuousclass,- loglaplaceobject 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(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. - Notes - The probability density function for - loglaplaceis:\[\begin{split}f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1} &\text{for } 0 < x < 1\\ \frac{c}{2} x^{-c-1} &\text{for } x \ge 1 \end{cases}\end{split}\]- for \(c > 0\). - loglaplacetakes- cas a shape parameter for \(c\).- The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the - locand- scaleparameters. Specifically,- loglaplace.pdf(x, c, loc, scale)is identically equivalent to- loglaplace.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.- Suppose a random variable - Xfollows the Laplace distribution with location- aand scale- b. Then- Y = exp(X)follows the log-Laplace distribution with- c = 1 / band- scale = exp(a).- References - T.J. Kozubowski and K. Podgorski, “A log-Laplace growth rate model”, The Mathematical Scientist, vol. 28, pp. 49-60, 2003. - Examples - >>> import numpy as np >>> from scipy.stats import loglaplace >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Get the support: - >>> c = 3.25 >>> lb, ub = loglaplace.support(c) - Calculate the first four moments: - >>> mean, var, skew, kurt = loglaplace.stats(c, moments='mvsk') - Display the probability density function ( - pdf):- >>> x = np.linspace(loglaplace.ppf(0.01, c), ... loglaplace.ppf(0.99, c), 100) >>> ax.plot(x, loglaplace.pdf(x, c), ... 'r-', lw=5, alpha=0.6, label='loglaplace 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 = loglaplace(c) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') - Check accuracy of - cdfand- ppf:- >>> vals = loglaplace.ppf([0.001, 0.5, 0.999], c) >>> np.allclose([0.001, 0.5, 0.999], loglaplace.cdf(vals, c)) True - Generate random numbers: - >>> r = loglaplace.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() 