Entropy Estimation of Inverse Weibull Distribution under Adaptive Type-II Progressive Hybrid Censoring Schemes

Gui, Rong Xu and Wenhao

doi:10.3390/sym11121463

Cited by 14 publications

(5 citation statements)

References 25 publications

(32 reference statements)

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“…In the existing literature, there have been significant advancements in the estimation of entropy functions for different distributions. Xu and Gui [13] discussed the estimation problem of entropy for the two-parameter inverse Weibull distribution under an adaptive Type-II progressive hybrid censoring scheme. Chacko and Asha [14] discussed the entropy estimation problem for the generalized exponential distribution based on record values.…”

Section: Shannon Entropy Of Grd(σ β)mentioning

confidence: 99%

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Ren

Gong

Han

2023

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This paper investigates the problem of entropy estimation for the generalized Rayleigh distribution under progressively type-II censored samples. Based on progressively type-II censored samples, we first discuss the maximum likelihood estimation and interval estimation of Shannon entropy for the generalized Rayleigh distribution. Then, we explore the Bayesian estimation problem of entropy under three types of loss functions: K-loss function, weighted squared error loss function, and precautionary loss function. Due to the complexity of Bayesian estimation computation, we use the Lindley approximation and MCMC method for calculating Bayesian estimates. Finally, using a Monte Carlo statistical simulation, we compare the mean square errors to examine the superiority of maximum likelihood estimation and Bayesian estimation under different loss functions. An actual example is provided to verify the feasibility and practicality of various estimations.

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Section: Shannon Entropy Of Grd(σ β)mentioning

confidence: 99%

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Ren

Gong

Han

2023

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“…where V( θNR ) = I −1 obs ( θNR ) is given by (19). Upon using the approximate variances of ŜNR (t) given above, the 100(1 − α)% asymptotic confidence intervals of S(t) with respect to NR method is given by…”

Section: Asymptotic Confidence Intervalsmentioning

confidence: 99%

“…According to the adaptive Type-II censored scheme, Sewailem and Baklizi [18] investigated the ML and Bayes estimates for the log-logistic distribution parameters. The estimations of entropy for inverse Weibull distributions using the adaptive Type-II censored scheme were developed by Xu and Gui [19]. The parameters of an exponentiated inverted Rayleigh model were calculated by Panahi and Moradi [20].…”

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confidence: 99%

Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications

2022

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This study uses the adaptive Type-II progressively censored competing risks model to estimate the unknown parameters and the survival function of the Gompertz distribution. Where the lifetime for each failure is considered independent, and each follows a unique Gompertz distribution with different shape parameters. First, the Newton-Raphson method is used to derive the maximum likelihood estimators (MLEs), and the existence and uniqueness of the estimators are also demonstrated. We used the stochastic expectation maximization (SEM) method to construct MLEs for unknown parameters, which simplified and facilitated computation. Based on the asymptotic normality of the MLEs and SEM methods, we create the corresponding confidence intervals for unknown parameters, and the delta approach is utilized to obtain the interval estimation of the reliability function. Additionally, using two bootstrap techniques, the approximative interval estimators for all unknowns are created. Furthermore, we computed the Bayes estimates of unknown parameters as well as the survival function using the Markov chain Monte Carlo (MCMC) method in the presence of square error and LINEX loss functions. Finally, we look into two real data sets and create a simulation study to evaluate the efficacy of the established approaches.

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“…The parameters of IWD were estimated under adaptive type-II progressive hybrid censoring scheme, see Nassar and Abo-Kasem [4]. For entropy estimation of the IWD, see Xu and Gui [5], and for modelling reliability data, see Alkarni et al [6]. The random variable T has an inverse Weibull random variable if the probability density function (PDF) is f (t) = αβt −(β+1) e −αt −β , α, β > 0, t > 0, (1) where α and β are the scale and shape parameters, respectively.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Type-II Hybrid Progressive Censoring Samples for Statistical Inference of Comparative Inverse Weibull Distributions

Al-Essa,

Soliman,

Abd-Elmougod

et al. 2023

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Recently, there has been a lot of interest in comparative life testing for items under jointly censored schemes for products from multiple production lines. The inverse Weibull distribution (IWD) is commonly used in life testing and reliability theory. In this paper, we address the problem of statistical inference from comparative inverse Weibull distributions under joint samples. An adaptive type-II hybrid progressive censoring scheme (HPCS) is used to save the balance between the ideal test time and the number of observed failures. Under the adaptive type-II HPCS, unknown parameters of the inverse Weibull populations are estimated using both maximum likelihood and Bayesian approaches. Asymptotic confidence intervals are established using the observed Fisher information matrix and bootstrap confidence intervals. We suggest using Markov chain Monte Carlo (MCMC) techniques to compute credible intervals under independent gamma priors. Using Monte Carlo simulations, all theoretical conclusions are tested and contrasted. For illustration purposes, an actual sample from comparative populations is analysed.

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Entropy Estimation of Inverse Weibull Distribution under Adaptive Type-II Progressive Hybrid Censoring Schemes

Cited by 14 publications

References 25 publications

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications

Adaptive Type-II Hybrid Progressive Censoring Samples for Statistical Inference of Comparative Inverse Weibull Distributions

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