Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

TL;DR

This paper introduces generalized Mittag-Leffler distributions and autoregressive processes, exploring their properties and applications in physics, astrophysics, and time series modeling, with potential benefits in diverse scientific fields.

Contribution

It develops new autoregressive models based on generalized Mittag-Leffler distributions and discusses their properties and applications in various scientific domains.

Findings

Introduced geometric generalized Mittag-Leffler distributions with specific Laplace transforms.

Developed first-order autoregressive time series models using Mittag-Leffler distributions.

Explored applications in astrophysics, space sciences, meteorology, finance, and reliability modeling.

Abstract

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},0<\alpha\le 2,\beta>0$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.