Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches

Soliman, Ahmed A.; Abdellah, Ahmed H.; Sultan, Khalaf S.

doi:10.1016/j.csda.2005.12.020

Cited by 88 publications

(41 citation statements)

References 12 publications

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“…If H(σ, λ) = σ, then we obtain the Bayes estimatorsσ S andσ L , whereas if H(σ, λ) = λ, then we get H S (σ, λ) =λ S and H L (σ, λ) =λ L , respectively. The ratios of integrals in (4.5) and (4.6) do not to take a closed form; therefore, we consider Lindley's approximation technique (Lindley, 1980) that technique has been widely used (see, for example, Howlader and Hossain, 2002;Kundu and Gupta, 2005;Soliman et al, 2006). Based on Lindley's approximation, we have the following Bayes estimators of σ and λ under the SELF:σ…”

Section: Lindley's Approximationmentioning

confidence: 99%

“…Jaheen (2003) derived Bayes estimators of unknown parameters of the Gompertz distribution based on upper record values and obtained prediction bounds for future upper record values. Soliman et al (2006) obtained Bayes estimators based on record statistics for two unknown parameters of the Weibull distribution. Ahmadi and Balakrishnan (2011) have recently discussed the prediction of future order statistics based on the largest and smallest observations at the time of a new record.…”

Section: Introductionmentioning

confidence: 99%

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An Analysis of Record Statistics based on an Exponentiated Gumbel Model

Kang¹,

Seo²,

Kim

2013

Communications for Statistical Applications and Methods

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This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

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Section: Lindley's Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Analysis of Record Statistics based on an Exponentiated Gumbel Model

Kang¹,

Seo²,

Kim

2013

Communications for Statistical Applications and Methods

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“…To implement the calculations in this subsections, it is necessary to elicit the values of first ( , )   , see [34], which is given using (25) by nalysis r illustrative purposes, we performed a real data analysis. The original data is a subset of data reported by [6,36], represent the survival times in years of a gro f patients g 1.099.…”

Section: Symmetric Bayes Estimationmentioning

confidence: 99%

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Abushal¹

2011

OJS

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This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators have been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.

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“…[15] developed prediction bounds for future generalized exponential lower records by using Bayes and empirical Bayes techniques. [20] discussed the Bayesian analysis in the context of records from the twoparameter WE distribution through using a discrete prior for the shape parameter. Bayesian estimation and prediction for some life distributions based on record values, including Exponential, Weibull, Pareto and Burr type XII, are discussed in [2].…”

Section: Introductionmentioning

confidence: 99%

One-sequence and two-sequence prediction for future Weibull records

Bdair¹,

Raqab²

2016

JSTA

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Based on record data, prediction of the future records from the two-parameter Weibull distribution is studied. First we consider the sampling based procedure to compute the Bayes estimates and also to construct symmetric credible intervals. Secondly, we consider one-sequence and two-sequence Bayes prediction of the future records based on some observed records. The Monte Carlo algorithms are used to compute simulation consistent predictors and prediction intervals for future unobserved records. A numerical simulation study is conducted to compare the different methods and a real data set involving the annual rainfall recorded at Los Angeles Civic Center during 132 years is analyzed to illustrate the procedures developed here.

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Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches

Cited by 88 publications

References 12 publications

An Analysis of Record Statistics based on an Exponentiated Gumbel Model

An Analysis of Record Statistics based on an Exponentiated Gumbel Model

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

One-sequence and two-sequence prediction for future Weibull records

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