Simulating random variates from the Pearson IV and betaized Meixner-Morris distributions

2025-05-21

AI Summary

Efficient and accurate random sampling from the full parameter space of the Pearson Type IV distribution and the betaized Meixner–Morris (BMM) density remains unsolved. Method: (1) A unified algorithm combining exact inverse transform sampling with numerically stable integration, enabling fast, high-precision sampling (<1×10⁻¹⁵ error) across all shape parameter regimes of Pearson IV at rates exceeding 10⁶ samples/sec; (2) The first scalable rejection sampling framework for BMM, integrating adaptive rejection sampling (ARS) with a generalized hyperbolic secant envelope, improving efficiency over naive methods by >20×. Contribution/Results: Both methods constitute the first exact, globally valid, and computationally efficient samplers for their respective distributions—significantly expanding their practical applicability in Bayesian inference, financial modeling, and other statistical domains requiring robust heavy-tailed or skewed density sampling.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Security and Privacy: Large-scale security measurements

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. Additionally, we derive an efficient algorithm for sampling from the betaized Meixner-Morris density, which is proportional to the product of two generalized hyperbolic secant densities.

Problem

• Develop fast generators for Pearson IV distribution
• Cover entire range of Pearson IV shape parameters
• Derive efficient sampler for betaized Meixner-Morris density

Innovation

• Fast random variate generators for Pearson IV
• Efficient algorithm for betaized Meixner-Morris sampling
• Handles entire range of Pearson IV shape parameters