Statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data

A right truncated distribution called Right Truncated Fréchet -Weibull distribution with its mathematical forms of density, cumulative, survival and reverse hazard functions were provided in this paper. Statistical properties such as moments, quantile function, mode and moment generating function were studied as well as obtaining special cases to other truncated distributions. Maximum likelihood method used to estimate parameters numerically for randomly generated dataset and real-world data.

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“…If log L(x) has multiple local maxima, the highest solution is obtained. For more information, see [4].…”

Section: Parameters Estimationmentioning

confidence: 99%

Right Truncated Fréchet-Weibull Distribution: Statistical Properties and Application

Teamah

Elbanna

Gemeay

2020

Delta Journal of Science

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“…proof Mohie El-Din et al [16] and Ghitany et al [17] studied the existence and uniqueness of the MLEs for the parameters of GOM (α, β) based on progressive Type-II censored samples. They proved that J(α) is a decreasing function by…”

Section: The Existence and Uniqueness Of The Mlesmentioning

confidence: 99%

“…Chang and Tsai [14] introduced point and interval estimation for the Gompertz distribution under progressive Type-II while, Wu et al [15] gives the parameter estimates for the Gompertz distribution using the least squares method. Recently Mohie El-Din et al [16] made statistical inference for the Gompertz distribution based on progressive type-II hybrid censored data.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

El-Din

Abu‐Moussa

2018

Journal of the Egyptian Mathematical Society

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In this paper, we make a statistical inference for the Gompertz distribution based on multiply Type-I censored data, where we determine a censoring time point for each unit in the life time test. Estimation of the parameters is obtained using maximum likelihood method and Bayesian method, also the asymptotic confidence intervals for the parameters are constructed based on the approximate of the Fisher information matrix. The necessary condition for existence and uniqueness of the maximum likelihood estimators is discussed. The Bayesian estimates are obtained depending on the squared error loss function, linear exponential loss function and the generalized entropy loss function. The One-sample Bayesian prediction intervals are constructed for the unobserved lifetimes in the same sample. A real data example is presented to illustrate the methods of inference developed here. Finally, the simulation study is executed to compare the performance of the proposed methods.

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“…It was also found to be useful in medical sciences because it gives a good fit to data coming from clinical trials on ordered subjects [2]. Gompertz distribution has been extensively studied in the literature (see, for example, El-Din et al [3] and the reference therein). is paper focuses on the threeparameter generalized Gompertz distribution, which was proposed by El-Gohary et al [4].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

Obeidat

Al‐Nasser

Al-Omari

2020

Journal of Probability and Statistics

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This paper studies estimation of the parameters of the generalized Gompertz distribution based on ranked-set sample (RSS). Maximum likelihood (ML) and Bayesian approaches are considered. Approximate confidence intervals for the unknown parameters are constructed using both the normal approximation to the asymptotic distribution of the ML estimators and bootstrapping methods. Bayes estimates and credible intervals of the unknown parameters are obtained using differential evolution Markov chain Monte Carlo and Lindley’s methods. The proposed methods are compared via Monte Carlo simulations studies and an example employing real data. The performance of both ML and Bayes estimates is improved under RSS compared with simple random sample (SRS) regardless of the sample size. Bayes estimates outperform the ML estimates for small samples, while it is the other way around for moderate and large samples.

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Statistical inference for the Gompertz distribution based on Type-II progressively hybrid censored data

Cited by 20 publications

References 1 publication

Right Truncated Fréchet-Weibull Distribution: Statistical Properties and Application

Right Truncated Fréchet-Weibull Distribution: Statistical Properties and Application

Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

Estimation of Generalized Gompertz Distribution Parameters under Ranked-Set Sampling

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