Estimation of Parameters of Life From Progressively Censored Data Using Burr-XII Model

Soliman, Ahmed A.

doi:10.1109/tr.2004.842528

Cited by 162 publications

(75 citation statements)

References 26 publications

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“…Being symmetric, the SE loss equally penalizes over-and under-estimation of the same magnitude. A useful asymmetric loss known as the LINEX loss function, was introduced by [28], and was widely used in several papers, see for example, [5,6,10,11,[28][29][30]. This function rises approximately exponentially on one side of zero, and approximately linearly on the other side.…”

Section: The Loss Functionmentioning

confidence: 99%

“…[1] mentioned that the inference is feasible, and practical when the sample data are gathered according to a Type-II progressively censored study experimental scheme. Statistical inferences on the parameters of failure time distributions under progressive censoring have been studied by several authors such as [1][2][3][4][5][6][7][8][9][10][11][12]. A recent account on progressive censoring schemes can be found in the book by [13], or in the excellent review by [14].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Loss Functionmentioning

confidence: 99%

Section: Introductionmentioning

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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“…Shao et al (2004b) studied models for extremes using the BXII distribution with application to flood frequency analysis. According to Soliman (2005), this distribution covers the curve shape characteristics for a large number of distributions. The versatility and flexibility of the BXII distribution turns it quite attractive as a tentative model for fitting data real whose underlying distribution is unknown.…”

Section: Introductionmentioning

confidence: 99%

The Burr XII Negative Binomial Distribution with Applications to Lifetime Data

Ramos¹,

Percontini²,

Cordeiro³

et al. 2015

IJSP

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A five-parameter model, called the Burr XII negative binomial distribution, is defined and studied. The new model contains as special cases some important lifetime distributions discussed in the literature, such as the log-logistic, Weibull, Pareto type II and Burr XII distributions, among several others. We derive the ordinary and incomplete moments, generating and quantile functions, mean deviations, reliability and two types of entropy. The order statistics and their moments are investigated. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to real data demonstrates that the new distribution can provide a better fit than other classical lifetime models.

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“…Shao (2004) discussed maximum likelihood estimation of its parameters and Shao et al (2004) studied models for extremes based on the BXII distribution with application to flood frequency analysis. According to Soliman (2005), this model generalizes a large number of distributions. Its versatility and flexibility turns it quite attractive as a tentative model for lifetime data.…”

Section: Introductionmentioning

confidence: 99%

The Exponentiated Burr XII Poisson Distribution with Application to Lifetime Data

Silva¹,

Gomes-Silva²,

Ramos³

et al. 2015

IJSP

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A five-parameter distribution, called the exponentiated Burr XII Poisson distribution, is defined and studied. The model has as special sub-models some important lifetime distributions discussed in the literature, such as the logistic, log-logistic, Weibull, Burr XII and exponentiated Burr XII distributions, among several others. We derive the ordinary and incomplete moments, generating and quantile functions, Bonferroni and Lorenz curves, mean deviations, reliability and two types of entropy. The order statistics and their moments are investigated. The method of maximum likelihood is proposed for estimating the model parameters. We obtain the observed information matrix. An application to a real data set demonstrates that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis.

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Estimation of Parameters of Life From Progressively Censored Data Using Burr-XII Model

Cited by 162 publications

References 26 publications

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

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

The Burr XII Negative Binomial Distribution with Applications to Lifetime Data

The Exponentiated Burr XII Poisson Distribution with Application to Lifetime Data

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