Generalized order statistics from exponential distribution

Ahsanullah, Mohammad

doi:10.1016/s0378-3758(99)00068-3

Cited by 70 publications

(34 citation statements)

References 5 publications

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“…Substituting from (4) and (5) into (3), the likelihood function is then given by (16) The log-likelihood function of is obtained from (16) as (17) To find the value of that maximizes (17), we differentiate (17) with respect to and set the resulting equation to zero. Therefore the MLE of θ is (18) By the invariance property of the ML estimators, the ML estimator for is obtained from Equation (8) as (19) It can be notice that follows the chi-square distribution with degrees of freedom, denoted by , see for instance Ahsanullah [18] and Ahmadi et al [15].…”

Section: Cmentioning

confidence: 99%

Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Soliman¹

2014

AJTAS

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Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C . The MLE and the Bayesian estimators of C are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.

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Section: Cmentioning

confidence: 99%

Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Soliman¹

2014

AJTAS

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“…Ahsanullah (1996;2000), Kamps and Gather (1997), Cramer and Kamps (2000), Habibullah and Ahsanullah (2000), Jaheen (2002;2005a), AL-Hussaini and Ahmad (2003), AL-Hussaini (2004), Ahmad (2007;2008), Aboeleneen (2010), Abushal (2006-2010), ), Abu El Fotouh (2011 and Ateya and Ahmad (2011) among others, utilized the (GOS's) in their Works.…”

Section: −T α and H(·) = F (·)mentioning

confidence: 99%

Bayesian Prediction Based on Generalized Order Statistics from a Mixture of Two Exponentiated Weibull Distribution Via MCMC Sumulation

Abushal¹,

AL-Zaydi²

2012

IJSP

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This paper is concerned with the problem of obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two exponentiated Weibull (MTEW) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values.

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“…A variety of order models of random variables is contained in this concept. [2], [3] discussed gOS from exponential and power function distributions. [4] Obtained some recurrence relations of moments for order statistics from generalized exponential distribution (Gexp).…”

Section: Introductionmentioning

confidence: 99%

Inference for generalized exponential distribution based on generalized order statistics

Afify¹

2015

IJAMR

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Generalized order statistics from exponential distribution

Cited by 70 publications

References 5 publications

Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Bayesian Prediction Based on Generalized Order Statistics from a Mixture of Two Exponentiated Weibull Distribution Via MCMC Sumulation

Inference for generalized exponential distribution based on generalized order statistics

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