A Study of the DAGUM Model for the Family of Exponential Distributions

Abstract

Real-world occurrences are frequently described using statistical distributions. The newlinedeveloping theory of statistical distributions is expansively researched and new distributions newlineare shaped as result of their use. In the field of statistics, there is still a lot of interest in creating newlinemore adaptable statistical distributions. Numerous generalised distribution classes have been newlinecreated and used to explain a range of phenomena. These generalised distributions all share newlinethe characteristic of having extra parameters. Four-parameter distributions should be adequate newlinefor the majority of real applications according to authors contend that a minimum of three newlinefactors is required, but they questioned whether adding a fifth or sixth parameter would newlineoutcome in any discernible improvement. newlinePresent research work, framed a new lifetime distribution named Exponentiated newlineExponential Weibull-Dagum distribution (EEWD), derived from T-R{Y} combined three newlinedistributions, in this case Dagum distribution worked as baseline and Y, where the QntF of Y newlineis used as a frame to hold the CDF of R, which is being transformed by T, with some newlineparameters of each distribution having outcome on the newly originated distribution. This newlinedistribution can be obtained through a straightforward transformation of a WRV (Weibull newlinerandom variable). Its PDF exhibits a high degree of flexibility, capable of taking on equal, newlineleft-skewed, right-skewed. The hazard function of this distribution can vary as well showed, newlineincreasing, decreasing, upside-down bathtub patterns. Derived various key properties, newlineincluding specific formulas for QntF (quantile function), ordinary and incomplete moments, newlineand probability-weighted moments. Additionally, provided obvious expressions for Shannon newlineentropies. Distribution of order statistics is expressed as combination of Dagum densities. newlineEstimate the model s parameters, we employ maximum likelihood estimation and newlinedemonstrate its usefulness through a simulation study and real data applications.