scipy.stats.tukeylambda — SciPy v1.16.2 Manual (original) (raw)

scipy.stats.tukeylambda = <scipy.stats._continuous_distns.tukeylambda_gen object>[source]#

A Tukey-Lamdba continuous random variable.

As an instance of the rv_continuous class, tukeylambda 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.

Methods

Notes

A flexible distribution, able to represent and interpolate between the following distributions:

• Cauchy (\(lambda = -1\))
• logistic (\(lambda = 0\))
• approx Normal (\(lambda = 0.14\))
• uniform from -1 to 1 (\(lambda = 1\))

tukeylambda takes a real number \(lambda\) (denoted lamin the implementation) as a shape parameter.

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, tukeylambda.pdf(x, lam, loc, scale) is identically equivalent to tukeylambda.pdf(y, lam) / 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.

Examples

import numpy as np from scipy.stats import tukeylambda import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1)

Get the support:

lam = 3.13 lb, ub = tukeylambda.support(lam)

Calculate the first four moments:

mean, var, skew, kurt = tukeylambda.stats(lam, moments='mvsk')

Display the probability density function (pdf):

x = np.linspace(tukeylambda.ppf(0.01, lam), ... tukeylambda.ppf(0.99, lam), 100) ax.plot(x, tukeylambda.pdf(x, lam), ... 'r-', lw=5, alpha=0.6, label='tukeylambda 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 = tukeylambda(lam) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of cdf and ppf:

vals = tukeylambda.ppf([0.001, 0.5, 0.999], lam) np.allclose([0.001, 0.5, 0.999], tukeylambda.cdf(vals, lam)) True

Generate random numbers:

r = tukeylambda.rvs(lam, 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()