Summary Of Four Generalized Exponential Models (GEM) For Continuous Probability Distributions

TL;DR

This paper introduces four new generalized exponential models for continuous probability distributions, extending classical models and providing comprehensive distributional measures and estimation techniques.

Contribution

It presents four novel generalized exponential models for univariate continuous distributions with detailed derivations and applications, expanding existing distribution families.

Findings

Derived four new probability models generalizing classical distributions

Provided formulas for moments, skewness, kurtosis, and other measures

Outlined maximum likelihood estimation for these models

Abstract

Four new probability models are derived which generalize the common univariate continuous distributions. Classical distributional measures are derived from Hoel, et al., Introduction to Probability Theory, 1971. Measures include probability density function, moments generating function, cumulative distribution function,derivatives, inverse distributions, skewness, kurtosis, change of variable distributions, log distributions. Maximum likelihood estimation technique is briefly outlined. Appendices describe applications. Errata/addenda sheet included.