The gompertz exponential pareto distribution with the properties and applications to bladder cancer and hydrological datasets

Abstract

Many existing distributions in literatures does not have the modeling fits capacity to adequately describe the real-life phenomena. The Exponential Pareto (EP) distribution has further gained some generalizations among several authors using different generator techniques with an aim to obtain a new distribution with greater flexibility. This article proposes Gompertz Exponential Pareto (GEP) distribution using the Gompertz generator. Findings from the study revealed some lifetime distributions as special cases and mathematical properties of the distribution investigated including the mean, variance, coefficient of variation, quantile, moment, moment generating function and, order statistics. The distribution can be positively or negatively skewed. It is unimodal with failure rates whose shapes could be reversed J bathtub, constant, decreasing and, increasing and the parameters were estimated using maximum likelihood estimation approach. Applications to two real-life datasets revealed the ability of GEP distribution to provide more flexibilities and better fit to the dataset compared to some previously proposed distributions for the data. The results also revealed that GEP had the superior performance over other generalizations of EP distribution existing in literatures and the performance has further strengthened the usefulness of the Gompertz-generator technique.

Modeling Extreme Stochastic Variations using the Maximum Order Statistics of Convoluted Distributions

“…The standard and widely used goodness-of-fit-statistics for model selection criteria by researchers in making decision about competing distributions are -loglikelihood (-LL), Akaike information criterion (AIC), Bayesian information criterion (BIC), Consistent Akaike Information Criterion (CAIC), Hannan-Quinn Information Criteria (HQIC), the Kolmogorov-Smirnov (K-S) statistics and the P-value. They can be found in several related works including [24], [50], [51] and most recently in [56]. The goodnessof-fit-statistics are defined as:…”

“…The convolution of exponential and Pareto distributions by [18] produced the Exponential Pareto (EP) distribution which [19,20,21,22,23,24] further generalized and studied with diverse applications using different approaches. [25] proposed Transmuted Topp-Leone extended Frechet distribution for modeling extreme value of dataset with some application.…”

Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset

“…𝛽 ,k,𝜃 are the parameters of the distribution The EP distribution has further gained extensive studies with applications from Luguterah and Nasiru (2015) , using the quadratic rank transmutation map (QRTM) to develop the Transmuted Exponential Pareto (TEP) distribution, the beta-G framework was used by Aryal (2019) and later by Rashwan and Kamel (2020) for the construction of Beta Exponential Pareto (BEP) model. Kumaraswamy Exponential Pareto (KEP) distribution was introduced by Elbatal and Aryal (2017) using the Kum-G technique and most recently, the Gompertz-G technique was explored for developing the Gompertz Exponential Pareto distribution by (Adeyemi et al, 2021) . Dikko and Faisal (2017) proposed the generalized exponential Weibull (GEW) distribution and the Topp Leone Weibull distribution (TLWD) was introduced by (Tuoyo et al, 2021) .…”