The New Mixed Hypoexponential-G Family

TL;DR

This paper introduces a new class of mixed distributions formed as linear combinations of existing distributions, including the development of the New Mixed T-G family and the Hypoexponential G-Family, with detailed characteristics and estimation methods.

Contribution

It defines and characterizes a novel class of mixed distributions and constructs the New Mixed T-G family and Hypoexponential G-Family, expanding the tools for modeling complex stochastic processes.

Findings

Derived PDFs, CDFs, hazard functions, and moments for the new distributions.

Studied maximum likelihood and method of moments estimators.

Provided theoretical properties and potential applications.

Abstract

Through viewing out the literature, many generated distributions took a new special form of probability density function (PDF) in which it is written as a linear combination of n other distributions. Therefore, we define in this paper a new type of distributions called "The New Mixed Distribution" form in which a distribution is written as a linear combination of n others and derive its characteristics. Second we construct "The New Mixed T-G family" a family of distributions following another new defined type "The New Mixed T-G Distribution". Third, we generate "The New Mixed Hypoexponential G-Family" out of 6 new mixed distributions with characterizing their PDFs, CDFs, hazard rate and reliability functions, MGF, and nth moment, and studying their maximum likelihood estimator and method of moments.