Method for Generating Distributions and Classes of Probability Distributions: The Univariate Case

TL;DR

This paper introduces a method for constructing new probability distributions and classes by combining known distributions with monotonic functions, expanding the toolkit for probabilistic modeling.

Contribution

It presents a novel method to generate probability distributions from known distributions and monotonic functions, broadening existing distribution classes.

Findings

Generated new distribution classes described in literature

Analyzed support and nature of the constructed distributions

Demonstrated the method's ability to broaden distribution construction

Abstract

In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from pre-defined monotonic functions and from known distributions. With the use of this method, we can obtain different classes of probability distributions described in literature. Beside these results, we could obtain results on the support and nature of the generated distributions.