On some mixtures of the Kies distribution

TL;DR

This paper investigates mixtures of Kies distributions, analyzing their probabilistic properties, convergence conditions, and special cases like bimodal and multimodal distributions, with applications demonstrated through numerical experiments.

Contribution

It introduces new insights into the properties and convergence of Kies distribution mixtures, including special cases and real-world applications.

Findings

Conditions for convergence of Kies mixtures established

Analysis of bimodal and multimodal distribution properties

Numerical experiments demonstrate practical applications

Abstract

The purpose of this paper is to explore some mixtures of Kies distributions -- discrete and continuous. The last ones are also known as compound distributions. Some conditions for convergence are established. We study the probabilistic properties of these mixtures. Special attention is taken to the so-called Hausdorff saturation. Several particular cases are considered -- bimodal and multimodal distributions, and mixtures based on binomial, geometric, exponential, gamma, and beta distributions. Some numerical experiments for real-life tasks are provided.