The Gompertz Fréchet distribution: Properties and applications

Oguntunde, Pelumi E.; Khaleel, Mundher A.; Ahmed, Mohammed T.; Okagbue, Hilary I.

doi:10.1080/25742558.2019.1568662

Cited by 16 publications

(8 citation statements)

References 11 publications

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“…Let , ,…, be a strength random sample of size n from GF( ) where is an unknown parameter and are known. Then, the likelihood function is given by [5]:…”

Section: -1-maximum Likelihood Estimation (Mle) Methodsmentioning

confidence: 99%

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Gompertz Fréchet stress-strength Reliability Estimation

Jabr

Karam

2021

eijs

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In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.

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“…Let , ,…, be a strength random sample of size n from GF( ) where is an unknown parameter and are known. Then, the likelihood function is given by [5]:…”

Section: -1-maximum Likelihood Estimation (Mle) Methodsmentioning

confidence: 99%

“…and * + … (4) respectively , where is the scale parameter and is the shape parameter. The CDF of the Gompertz Fréchet (GF) distribution is obtained by substituting equation (3) in equation ( 1), given by [5]:…”

Section: Jabr and Karammentioning

confidence: 99%

Gompertz Fréchet stress-strength Reliability Estimation

Jabr

Karam

2021

eijs

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“…Let … be strength random sample of size n from θ where θ is unknown parameter and are known. the likelihood function given by [12] … Then by substitute equations (8) , ( 9) and (10) in equation ( 7) we get :…”

Section: Maximum Likelihood (Mle)mentioning

confidence: 99%

Estimating the Reliability of a Component between Two Stresses from Gompertz-Frechet Model

Adnan¹,

Karam²

2021

Al-Qadisiyah Journal of Pure Science

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In this paper, the reliability of the stress-strength model is derived for probability P( <X< ) of a component strength X between two stresses , , when X and , are independent Gompertz Fréchet distribution with unknown and known shape parameters and common known scale parameters. Different methods used to estimate R and Gompertz Fréchet distribution parameters which are [Maximum Likelihood, Least square, Weighted Least square, Regression and Ranked set sampling methods], and the comparison between these estimations by simulation study based on mean square error criteria. The comparison confirms that the performance of the maximum likelihood estimator works better than the other estimators.

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“…Mead et al [ 20 ] introduced the beta exponential Fréchet distribution. The properties of the Gompertz Fréchet distribution have been studied by Oguntunde et al [ 21 ]. An overview of the various estimators and applications for the Fréchet distribution has been discussed by Ramos et al [ 22 ].…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference under Censored Data for the New Exponential‐X Fréchet Distribution: Simulation and Application to Leukemia Data

Alzeley

Almetwally

Gemeay

et al. 2021

Computational Intelligence and Neuroscience

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In reliability studies, the best fitting of lifetime models leads to accurate estimates and predictions, especially when these models have nonmonotone hazard functions. For this purpose, the new Exponential-X Fréchet (NEXF) distribution that belongs to the new exponential-X (NEX) family of distributions is proposed to be a superior fitting model for some reliability models with nonmonotone hazard functions and beat the competitive distribution such as the exponential distribution and Frechet distribution with two and three parameters. So, we concentrated our effort to introduce a new novel model. Throughout this research, we have studied the properties of its statistical measures of the NEXF distribution. The process of parameter estimation has been studied under a complete sample and Type-I censoring scheme. The numerical simulation is detailed to asses the proposed techniques of estimation. Finally, a Type-I censoring real-life application on leukaemia patient’s survival with a new treatment has been studied to illustrate the estimation methods, which are well fitted by the NEXF distribution among all its competitors. We used for the fitting test the novel modified Kolmogorov–Smirnov (KS) algorithm for fitting Type-I censored data.

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The Gompertz Fréchet distribution: Properties and applications

Cited by 16 publications

References 11 publications

Gompertz Fréchet stress-strength Reliability Estimation

Gompertz Fréchet stress-strength Reliability Estimation

Estimating the Reliability of a Component between Two Stresses from Gompertz-Frechet Model

Statistical Inference under Censored Data for the New Exponential‐X Fréchet Distribution: Simulation and Application to Leukemia Data

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