On Progressive Type-II Censored Samples from Alpha Power Exponential Distribution

Salah, Mukhtar M.

doi:10.1155/2020/2584184

Cited by 13 publications

(12 citation statements)

References 12 publications

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“…where = (θ 1 , θ 2 , α 1 , α 2 ) . The MLEs of the parameters θ t and α t , t = 1, 2 can be obtained by maximizing the log-likelihood function in (9) with respect to θ t and α t , t = 1, 2. Another way to acquire these estimates is to find the normal equations by getting the first partial derivatives of (9) with respect to θ t and α t and equating them to zero.…”

Section: Mlesmentioning

confidence: 99%

“…For an extensive review of progressively censoring, see Balakrishnan [7] and Balakrishnan and Cramer [8]. Under the assumption of APE distribution for lifetime observation, Salah [9] studied the estimation of the APE distribution using progressively Type-II censored data. Salah et al [10] investigated the APE distribution using Type-II hybrid censored samples.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

2022

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In reliability analysis and life testing studies, the experimenter is frequently interested in studying a specific risk factor in the presence of other factors. In this paper, the estimation of the unknown parameters, reliability and hazard functions of alpha power exponential distribution is considered based on progressively Type-II censored competing risks data. We assume that the latent cause of failures has independent alpha power exponential distributions with different scale and shape parameters. The maximum likelihood method is considered to estimate the model parameters as well as the reliability and hazard rate functions. The approximate and two parametric bootstrap confidence intervals of the different estimators are constructed. Moreover, the Bayesian estimation method of the unknown parameters, reliability and hazard rate functions are obtained based on the squared error loss function using independent gamma priors. To get the Bayesian estimates as well as the highest posterior credible intervals, the Markov Chain Monte Carlo procedure is implemented. A comprehensive simulation experiment is conducted to compare the performance of the proposed procedures. Finally, a real dataset for the relapse of multiple myeloma with transplant-related mortality is analyzed.

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Section: Mlesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

2022

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“…In this regard, Cohen [13] provided a progressive censored model for normal and exponential distribution using maximum likelihood estimators (MLE). Similarly, Salah [14] suggested progressive type-II censoring for alpha power exponential distribution under MLE. Liao and Gui [15] suggested the Bayesian estimates using progressively type-II censored samples for the Rayleigh distribution under various loss functions.…”

Section: Introductionmentioning

confidence: 99%

Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution

Liu

Khan

Anwar

et al. 2022

Mathematical Problems in Engineering

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The power function distribution is a flexible waiting time model that may provide better fit for some failure data. This paper presents the Bayes estimates of two-parameter power function distribution under progressive censoring. Different progressive censoring schemes have been used for the analysis. The Bayes estimates are obtained, using conjugate priors, under five loss functions including square error, precautionary, weighted, LINEX, and DeGroot loss function. The Gibbs sampling algorithm and Tierney and Kadane’s Approximation are used for the Bayes estimates of model parameters, reliability function, and stress-strength reliability. The comparison of the Bayes estimates is considered through the root mean squared errors. One real-life dataset is analyzed to illustrate the applications of proposed estimates. The results from the simulation study and real data analysis suggest that the Bayes estimation was more efficient for the progressive censoring schemes with all the withdrawals at the time of first failure.

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“…Salah [3] studied parameters estimation of APED under progressive Type-II censored scheme (PCS-Type II) using the MLE. Salah et al [4] considered parameter estimation of APED under Type-II hybrid censored scheme (HCS-Type II) using the MLE and expectation maximizations algorithm.…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis Based on Progressive Type‐I Censored Scheme from Alpha Power Exponential Distribution with Engineering and Medical Applications

Abo-Kasem

Sallam

Aljohani

et al. 2022

Journal of Mathematics

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Using a progressive Type-I censoring technique, this article will explore how to estimate unknown parameters of the alpha power exponential distribution (APED) (Type-I PCS). The squared error loss function and the LINEX loss function are used to get the maximum likelihood estimate as well as the Bayesian estimation of the unknown parameters, respectively. It was our intention to use the Markov chain Monte Carlo method in conjunction with the Bayes estimation strategy. We are able to calculate the approximately accurate confidence intervals for the parameters whose values are unknown. In addition to this, we discussed the estimation challenges of reliability and the hazard rate function of the APED while using Type-I PCS, as well as the approximate confidence intervals that relate to these problems. In the last step, the theoretical findings that were acquired are evaluated and compared with the distributions of all of its rivals by making use of two actual datasets that represent the disciplines of engineering and medicine.

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On Progressive Type-II Censored Samples from Alpha Power Exponential Distribution

Abstract: In this paper the two-parameter α -power exponential distribution is studied. We study the two-parameter α -power exponential μ , λ … Show more

Cited by 13 publications

References 12 publications

Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data

Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution

Statistical Analysis Based on Progressive Type‐I Censored Scheme from Alpha Power Exponential Distribution with Engineering and Medical Applications

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