scipy.stats.loglaplace — SciPy v1.15.3 Manual (original) (raw)

scipy.stats.loglaplace = <scipy.stats._continuous_distns.loglaplace_gen object>[source]#

A log-Laplace continuous random variable.

As an instance of the rv_continuous class, loglaplace object 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 loglaplace is:

\[\begin{split}f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1} &\text{for } 0 < x < 1\\ \frac{c}{2} x^{-c-1} &\text{for } x \ge 1 \end{cases}\end{split}\]

for \(c > 0\).

loglaplace takes c as a shape parameter for \(c\).

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, loglaplace.pdf(x, c, loc, scale) is identically equivalent to loglaplace.pdf(y, c) / scale withy = (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 X follows the Laplace distribution with location a and scale b. Then Y = exp(X) follows the log-Laplace distribution with c = 1 / b and 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)

Calculate the first four moments:

c = 3.25 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 cdf and 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()

Methods