We define and study a three-parameter model with positive real support called the exponentiated generalized extended Pareto distribution. We provide a comprehensive mathematical treatment and prove that the formulas related to the new model are simple and manageable. We study the behaviour of the maximum likelihood estimates for the model parameters using Monte Carlo simulation. We take advantage of applied studies and offer two applications to real data sets that proves empirically the power of adjustment of the new model when compared to another twelve lifetime distributions.
Abstract: We introduce and study a new four-parameter lifetime model named the exponentiated generalized extended exponential distribution. The proposed model has the advantage of including as special cases the exponential and exponentiated exponential distributions, among others, and its hazard function can take the classic shapes: bathtub, inverted bathtub, increasing, decreasing and constant, among others. We derive some mathematical properties of the new model such as a representation for the density function as a double mixture of Erlang densities, explicit expressions for the quantile function, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R´enyi entropy, density of order statistics and reliability. We use the maximum likelihood method to estimate the model parameters. Two applications to real data illustrate the flexibility of the proposed model.
This paper presents a new generalization of the extended Gompertz distribution. We defined the so-called exponentiated generalized extended Gompertz distribution, which has at least three important advantages: (i) Includes the exponential, Gompertz, extended exponential and extended Gompertz distributions as special cases; (ii) adds two parameters to the base distribution, but does not use any complicated functions to that end; and (iii) its hazard function includes inverted bathtub and bathtub shapes, which are particularly important because of its broad applicability in real-life situations. The work derives several mathematical properties for the new model and discusses a maximum likelihood estimation method. For the main formulas related to our model, we present numerical studies that demonstrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the EGEG model. Three real- world data sets were used for applications in order to illustrate the usefulness of our proposal.