Generalized Gompertz -Generalized Gompertz Distribution Generalized Gompertz -Generalized Gompertz Distribution (original) (raw)
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Generalized Gompertz - Generalized Gompertz Distribution
Journal of Physics: Conference Series
In the present paper, we introduce a new generated family of continuous distributions based on generalized Gompertz distribution. Then generalized Gompertzgeneralized Gompertz distribution is proposed as a special case of this new family. The probability density, cumulative distribution, reliability and hazard rate functions are introduced. Additionally, the most essential statistical properties of this new distribution such as the mean, variance, coefficient of skewness, coefficient of kurtosis, characteristic function, quantiel, median, Shannon and relative entropies along with stress strength model are obtained.
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.
Generalized Gompertz-generalized inverse Weibull distribution
1ST SAMARRA INTERNATIONAL CONFERENCE FOR PURE AND APPLIED SCIENCES (SICPS2021): SICPS2021
In this paper, we present generalized Gompertz-generalized Inverse Weibull distribution (GGO-GIWD). Some properties of proposed distribution are derived. These properties are the reliability and hazard functions, rth raw moments, stress-strength reliability, Shannon entropy and relative entropy.
American Journal of Theoretical and Applied Statistics
We developed a five parameter distribution known as the Generalized Exponentiated Gompertz Makeham distribution which is quite flexible and can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters making it more effective in modeling survival data and reliability problems. Some comprehensive properties of the new distribution, such as closed-form expressions for the density function, cumulative distribution function, hazard rate function, moment generating function and order Statistics were provided as well as maximum likelihood estimation of the Generalized Exponentiated Gompertz Makeham distribution parameters and at the end, in order to show the distribution flexibility, an application using a real data set was presented.
2021
Statistical distributions are very useful in describing and predicting real world phenomena. In this paper, a new continuous model called Gompertz exponential distribution is defined and studied. Its resulting densities and statistical properties were carefully derived and the method of maximum likelihood was proposed in estimating the model parameters. A simulation on R was done to assess the performance of the parameters of the new model. Gompertz exponential distribution was illustrated with an application to real-life data. The result shows that Gompertz exponential distribution performs better than other three-parameter distributions such as Kumaraswamy–exponential distribution, Generalized Gompertz distribution, and Three-Parameter Lindley distribution
The Beta-Gompertz Distribution
In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as Beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, thekth order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher’s information matrix. A simulation study is performed in order to investigate the properties of the proposed estimator. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented.
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.
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
Exponentaited Generalized Weibull-Gompertz Distribution
This paper introduces studies on exponentaited generalized Weibull - Gompertz distribution EGWGD which generalizes a lot of distributions. Several properties of the EGWGD such as reversed (hazard) function, moments, maximum likelihood estimation, mean residual (past) lifetime, MTTF, MTTR, MTBF, maintainability, availability and order statistics are studied in this paper. A real data set is analyzed and it is observed that the present distribution can provide a better fit than some other very well-known distributions