Pareto probability distribution (type I)

This module implements functions for the Pareto distribution. The wikipedia article [1] refers to this as the Type I Pareto distribution, but this implementation includes a location parameter in addition to shape and scale parameters shown in the wikipedia page.

[1]

Pareto distribution, Wikipedia, https://en.wikipedia.org/wiki/Pareto_distribution

mpsci.distributions.pareto.cdf(x, b, loc=0, scale=1)

Cumulative distribution function for the Pareto distribution (type I).

mpsci.distributions.pareto.entropy(b, loc=0, scale=1)

Differential entropy of the Pareto distribution (type I).

mpsci.distributions.pareto.invcdf(p, b, loc=0, scale=1)

Inverse of the CDF of the Pareto distribution (type I).

mpsci.distributions.pareto.invsf(p, b, loc=0, scale=1)

Inverse of the survival function of the Pareto distribution (type I).

mpsci.distributions.pareto.logpdf(x, b, loc=0, scale=1)

Logarithm of the PDF for the Pareto distribution (type I).

mpsci.distributions.pareto.mean(b, loc=0, scale=1)

Mean of the Pareto distribution (type I).

mpsci.distributions.pareto.mle(x, *, b=None, loc=None, scale=None)

Maximum likelihood estimation for the Pareto distribution (type I).

x must be a sequence of numbers.

Currently the function does not implement a good heuristic for the starting point in the numerical solver. The default (1 for each parameter that is not fixed) is typically a bad guess and will likely result in the numerical solver failing to converge to a solution.

mpsci.distributions.pareto.nll(x, b, loc=0, scale=1)

Negative log-likelihood function for the Pareto distribution (type I).

x must be a sequence of numbers, and each value in x must greater than or equal to loc + scale.

mpsci.distributions.pareto.pdf(x, b, loc=0, scale=1)

Probability density function for the Pareto distribution (type I).

mpsci.distributions.pareto.sf(x, b, loc=0, scale=1)

Survival function for the Pareto distribution (type I).

mpsci.distributions.pareto.support(b, loc=0, scale=1)

Support of the Pareto distribution (type I).

mpsci.distributions.pareto.var(b, *, loc=0, scale=1)

Variance of the Pareto distribution (type I).