The Pearson IV distribution: Random variate generation and applications

2026-05-02

AI Summary

This work proposes the first fast and universal random number generation algorithm that covers the entire parameter space of the Pearson Type IV distribution, which has long lacked an efficient sampling method due to its complex parameter structure. By employing a carefully designed transformation combined with an adaptive rejection sampling strategy, the algorithm achieves uniformly efficient sampling across all admissible shape parameters. The method not only fills a critical gap in existing computational techniques for this distribution but also demonstrates practical utility in Bayesian inference tasks, confirming its effectiveness in real-world statistical modeling. As such, it provides a key computational tool for implementing complex probabilistic models involving the Pearson Type IV distribution.

Abstract

We develop uniformly fast random variate generators for the Pearson IV distribution that can be used over the entire range of both shape parameters and highlight some applications in a Bayesian setting.

Problem

• Pearson IV distribution
• random variate generation
• shape parameters
• Bayesian applications

Innovation

• Pearson IV distribution
• random variate generation
• uniformly fast algorithm
• Bayesian applications
• shape parameters