A new weighted Gompertz distribution with applications to reliability data

Bakouch, Hassan S.; El-Bar, Ahmed M. T. Abd

doi:10.21136/am.2017.0277-16

Cited by 16 publications

(7 citation statements)

References 34 publications

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“…For most of the baseline cdf G(x) (and pdf g(x)), this integral can be evaluated directly or numerically with mathematical softwares as R, Matlab, Mathematica, and so on. Another approach is to consider the series expansion of f (x) given in (3).…”

Section: Moments and Moment Generating Functionmentioning

confidence: 99%

A weighted general family of distributions: Theory and practice

Bakouch

Chesneau

Enany

2020

Comp and Math Methods

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In this article, we introduce a new general family of distributions. The submodels of the general family accommodate various shapes of pdf and hazard rate, involving decreasing, increasing, bathtub and J-shapes. Hence, it can provide analysis for many practical datasets. Mathematical expressions for the family are obtained, including moments, moment generating and quantile functions, stochastic ordering, and entropy. Some submodels of the family are inserted based on the baseline distributions: Exponential, Gompertz, Lindley, and weight exponential distributions. Estimation of the model parameters is justified by the method of maximum likelihood. Capability of the family is shown by fitting three practical datasets to the mentioned submodels. K E Y W O R D Sfamily of distributions, goodness-of-fit statistics, statistical and reliability properties, weighted distributionsComp and Math Methods.

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Section: Moments and Moment Generating Functionmentioning

confidence: 99%

A weighted general family of distributions: Theory and practice

Bakouch

Chesneau

Enany

2020

Comp and Math Methods

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“…Some applications of this distribution can be found in Pollard and Valkovics [17]. An extension version of Gompertz is the weighted Gompertz distribution discussed by Bakouch and Abd El-Bar [18]. Now, we introduce the PDF and CDF of GWE-G distribution by using Equations (4)-(6) respectively, are:…”

Section: Generalized Weighted Exponential-gompertz Distributionmentioning

confidence: 99%

Generalized Weighted Exponential-Gompertez Distribution

Teamah¹,

El-Damrawy²,

Swan³

2020

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Statistical analysis of lifetime data is a significant topic in social sciences, engineering, reliability, biomedical and others. We use the generalized weighted exponential distribution, as a generator to introduce a new family called generalized weighted exponential-G family, and apply this new generator to provide a new distribution called generalized weighted exponential gombertez distribution. We investigate some of its properties, moment generating function, moments, conditional moments, mean residual lifetime, mean inactivity time, strong mean inactivity time, Rényi entropy, Lorenz curves and Bonferroni. Furthermore, in this model, we estimate the parameters by using maximum likelihood method. We apply this model to a real data-set to show that the new generated distribution can produce a better fit than other classical lifetime models.

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“…The Gompertz (G) distribution has the pdf g(x; λ, σ ) = λ σ e λ x− σ (e λ x −1) , x 0; λ, σ 0 (8) and its cdf is…”

Section: Weighted Exponential-gompertz Distributionmentioning

confidence: 99%

“…The Gompertz distribution plays an important role in modelling reliability, human mortality and actuarial data that have hazard rate with an exponential increase. An extension version of Gompertz is the weighted Gompertz distribution discussed by Bakouch and Abd El-Bar [8].…”

Section: Weighted Exponential-gompertz Distributionmentioning

confidence: 99%

On weighted exponential-Gompertz distribution: properties and application

El-Bar

Ragab

2019

Journal of Taibah University for Science

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In this paper, we introduce a new distribution generated by an integral transform of the probability density function of the weighted exponential distribution. This distribution is called the weighted exponential-Gompertz (WE-G). Its hazard rate function can be increasing and bathtubshaped. Several statistical properties of the new model are obtained, such as moment generating function, moments, conditional moments, mean inactivity time, mean residual lifetime and Rényi entropy. The maximum likelihood estimation of unknown parameters is introduced. A real data application demonstrates the performance of the new model.

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A new weighted Gompertz distribution with applications to reliability data

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Cited by 16 publications

References 34 publications

A weighted general family of distributions: Theory and practice

A weighted general family of distributions: Theory and practice

Generalized Weighted Exponential-Gompertez Distribution

On weighted exponential-Gompertz distribution: properties and application

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