A New Flexible Model for Three-Stage Phenomena: The Fragmented Kumar-Trapez Distribution

This article proposes a solution to the problem of limiting the representation of three-stage phenomena to linear forms and addresses the stability of the second stage by introducing a novel distribution, the Fragmented Kumar-Trapez (FKT) distribution, which includes two additional parameters beyond the parameters used for an existing standard model. These parameters provide flexibility to the density function, enabling it to model a wide range of shapes. This work contributes to the understanding of distributions whose probability density functions are divided into three parts, addressing key questions such as: How to handle such distributions? How to estimate the range parameters of the trapezoidal and proposed distributions using the maximum likelihood method? How to estimate the unknown parameters of the proposed distribution using both maximum likelihood and Bayesian methods? In addition, the article explores some of the mathematical properties of the proposed distribution. Finally, a simulation study on generated data and an illustrated example are conducted to demonstrate the practical importance of the FKT distribution. WinBUGS 1.4 program is used to illustrate the application of MCMC simulation.