Abstract
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.
Highlights
From both theoretical and applied perspectives, proposing new probability distributions is crucial to describing natural phenomena
We studied the structural properties of the exponentiated generalized extended Gompertz (EGEG) model and verified that all formulas associated with the proposed model are simple and manageable using computational resources
We investigate the behavior of the maximum likelihood estimators (MLEs) for the parameters of the EGEG model by generating from (11) samples sizes n = 100, 300, 500, 1000 with selected values for a, b, θ, γ and β
Summary
From both theoretical and applied perspectives, proposing new probability distributions is crucial to describing natural phenomena. For a given continuous baseline cdf G(x), and x ∈ R, those authors defined the exponentiated generalized class of distributions with two extra shape parameters a > 0 and b > 0 with cdf Thiago A. The first important point to note is the simplicity of equations (3) and (4) They have no complicated functions and will be always tractable when the cdf and pdf of the baseline distribution have simple analytic expressions. We define the exponentiated generalized extended Gompertz (EGEG) distribution by inserting (1) in equation (3). For the reasons listed above, we strongly believe it is important to study in detail the EGEG distribution We hope that this new distribution will be part of the arsenal of applied researchers and will be used in many practical situations.
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