The Comparative Study of Gompertz Exponential Distribution and other three Parameter Distributions of Exponential Class (original) (raw)

Exponentiated Gompertz Exponential (Egoe) Distribution: Derivation, Properties and Applications

Istatistik Journal of The Turkish Statistical Association, 2021

In this paper, a new probability distribution called Exponentiated Gompertz Exponential distribution was introduced which can help researchers to model different types of data sets. In proposed distribution we introduce a new shape parameter to Gompertz Exponential distribution, varied its tail weight such that it enhances its flexibility and performance. Furthermore, the maximum likelihood method was used in estimating the model's parameters. Simulation method was used to investigate the behaviours of the parameters of the proposed distribution; the results showed that the mean square error and standard error for the chosen parameter values decrease as the sample size increases. The proposed distribution was tested on real life data, the results showed that EGoE performed better than the existing distribution in the literature and a strong competitor to other distributions of the same class. The results also showed that the distribution can be used as an alternative model in modelling lifetime processes.

The Gompertz extended generalized exponential distribution: properties and applications

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2020

In this article, a new class of distribution of the exponential family of distributions called the Gompertz extended generalized exponential (G-EGE) distribution for life time processes is proposed. The mathematical properties of the G-EGE distribution such as reliability, hazard rate function, reversed hazard, cumulative, odd functions, quantiles function, kurtosis, skewness and order statistics were derived. The parameters of the G-EGE distribution were estimated using the maximum likelihood method. The e¢ ciency and ‡exibility of the G-EGE distribution were examined using a simulation study and a real life data application. The results revealed that the G-EGE distribution outperformed some existing distributions in terms of their test statistics.

Gompertz uniform {exponential} three parameter distribution and Application

Al-azhar scintifec of commarcial faculties , 2022

This paper introduces the Gompertz uniform exponential (GU{EXP}) three parameter distribution. Some mathematical properties of this distribution are studied. Density distribution, Reliability and hazard rate functions are obtained. The ordinary moments, quintile function, mean residual life, Renyi entropy are given. Four methods of estimation of the (GU{EXP}) distribution based on complete sampling and the MLE estimates based on censoring type | and || are given. Squared Bias and variances of the estimates via a Mont Carlo simulation study are computed. We introduced also a real data analysis.

The Gompertz distribution and maximum likelihood estimation of its parameters - a revision

Mpidr Working Papers, 2012

The Gompertz distribution is widely used to describe the distribution of adult deaths. Previous works concentrated on formulating approximate relationships to characterize it. However, using the generalized integro-exponential function exact formulas can be derived for its moment-generating function and central moments. Based on the exact central moments, higher accuracy approximations can be defined for them. In demographic or actuarial applications, maximum-likelihood estimation is often used to determine the parameters of the Gompertz distribution. By solving the maximum-likelihood estimates analytically, the dimension of the optimization problem can be reduced to one both in the case of discrete and continuous data.

The Gompertz Inverse Exponential (GoIE) distribution with applications

Cogent Mathematics & Statistics, 2018

The Gompertz inverse exponential (GoIE) distribution using the Gompertz generalized family of distributions was derived and introduced in this article. Some basic statistical properties of the model were derived and discussed in minute details. The model parameters were estimated using the maximum likelihood estimation method. Real-life applications were provided and the GoIE distribution provides better fits than the Gompertz exponential, Gompertz Weibull and Gompertz Lomax distributions.

Marshall Olkin exponential Gompertz distribution: Properties and applications

Periodicals of Engineering and Natural Sciences (PEN), 2020

Generalizing distribution is an important area in probability theory. Many distributions are not suitable for modeling data, that are either symmetric or heavily skewed. In this paper, a new compound distribution termed as Marshall Olkin Exponential Gompertz (MOEGo) is introduced. Several essential statistical properties of MOEGo distribution were studied and investigated. The estimation of distribution parameters was performed using the maximum likelihood estimation method. Two real data (symmetric and right-skewed) were adopted to illustrate the flexibility of MOEGo distribution. This flexibility enables the use of MOEGo distribution in various application areas.

THE EXPONENTIATED GENERALIZED EXTENDED GOMPERTZ DISTRIBUTION

Journal of Data Science, 2019

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.

Statistical properties and different methods of estimation of Gompertz distribution with application

Journal of Statistics and Management Systems

This article addresses the various properties and different methods of estimation of the unknown parameters of Gompertz distribution. Although, our main focus is on estimation from both frequentist and Bayesian point of view, yet, various mathematical and statistical properties of the Gompertz distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, stochasic ordering, stressstrength parameter, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, pseudo-moments estimators, modified moments estimators, L-moment estimators, percentile based estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, minimum spacing

A Modification of the Gompertz Distribution Based on the Class of Extended-Weibull Distributions

2020

This paper introduces a new four-parameter extension of the generalized Gompertz distributions. This distribution involves some well-known distributions such as extension of generalized exponential, generalized exponential, and generalized Gompertz distributions. In addition, it can have a decreasing, increasing, upside-down bathtub, and bathtub-shaped hazard rate function depending on its parameters. Some mathematical properties of this new distribution, such as moments, quantiles, hazard rate function, and reversible hazard rate function are obtained. In addition, the density function and the moments of the ordered statistics of this new distribution is provided. The parameters of model are estimated using the maximum likelihood method. Also, a real data set was used to illustrate the validity of the proposed distribution.

The Odd Generalized Exponential Gompertz Distribution

Applied Mathematics, 2015

In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtained some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.