Parameter estimation and prediction of order statistics for the Burr Type XII distribution with Type II censoring

Panahi, Hanieh; Sayyareh, Abdolreza

doi:10.1080/02664763.2013.838668

Cited by 33 publications

(18 citation statements)

References 18 publications

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“…For illustrative purpose, we will be considering the purification of the main component of spearmint essential oil with sample size n = 35 (see Panahi and Sayyareh, 2014). Before progressing further, we have first fitted the Burr XII distribution to the complete data-set.…”

Section: Discussionmentioning

confidence: 99%

Model Selection Based on Tracking Interval under Unified Hybrid Censored Samples

Sayyareh

Panahi

2018

JIRSS

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Abstract. The aim of statistical modeling is to identify the model that most closely approximates the underlying process. Akaike information criterion (AIC) is commonly used for model selection but the precise value of AIC has no direct interpretation. In this paper we use a normalization of a difference of Akaike criteria in comparing between the two rival models under unified hybrid censoring scheme. Asymptotic properties of maximum likelihood estimator based on the missing information principle are derived. Also, asymptotic distribution of the normalized difference of AICs is obtained and it is used to construct an interval, say tracking interval, for comparing the two competing models. Monte Carlo simulations are performed to examine how the proposed interval works for different censoring schemes. Two real datasets have been analyzed for illustrative purposes. The first is selecting between Weibull and generalized exponential distributions for main component of spearmint essential oil purification data. The second is the choice between models of the lifetimes of 20 electronic components.

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Section: Discussionmentioning

confidence: 99%

Model Selection Based on Tracking Interval under Unified Hybrid Censored Samples

Sayyareh

Panahi

2018

JIRSS

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“…where a 1 , b 1 , a 2 , b 2 , a 3 , and b 3 are positive hyper-parameters. The Gamma distributions have been suggested to be the prior distributions of Burr type XII distribution parameters in the literature, for example, Panahi and Sayyareh [23]. In practice, we can select the values of a j and b j for j = 1, 2, 3 such that the prior distribution has large variance and turns to be a non-informative prior.…”

Section: Bayesian Frameworkmentioning

confidence: 99%

Bayesian Inference of δ = P(X < Y) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples

et al. 2019

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Let X and Y follow two independent Burr type XII distributions and δ = P(X < Y). If X is the stress that is applied to a certain component and Y is the strength to sustain the stress, then δ is called the stress-strength parameter. In this study, The Bayes estimator of δ is investigated based on a progressively first failure-censored sample. Because of computation complexity and no closed form for the estimator as well as posterior distributions, the Markov Chain Monte Carlo procedure using the Metropolis-Hastings algorithm via Gibbs sampling is built to collect a random sample of δ via the joint distribution of the progressively first failure-censored sample and random parameters and the empirical distribution of this collected sample is used to estimate the posterior distribution of δ. Then, the Bayes estimates of δ using the square error, absolute error, and linear exponential error loss functions are obtained and the credible interval of δ is constructed using the empirical distribution. An intensive simulation study is conducted to investigate the performance of these three types of Bayes estimates and the coverage probabilities and average lengths of the credible interval of δ. Moreover, the performance of the Bayes estimates is compared with the maximum likelihood estimates. The Internet of Things and a numerical example about the miles-to-failure of vehicle components for reliability evaluation are provided for application purposes.

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“…Since then, the BTXII distribution has received considerable attention in reliability studies and failure time modeling due to its flexibility in shape. Various aspects and properties of the BTXII distribution with regard to other applications have been studied by many authors, including AL-Hussaini and Ali Mousa [18], Wingo [19], [20], Wang and Keats [21], Moore and Papadopoulos [22], Chen and Yeh [23], Tsai and Chiang [24], Lio et al [25], Lio and Tsai [26], Panahi and Sayyareh [27], and Srivastava and Mittal [28]. Connections of the BTXII distribution with various other distributions have been studied by Tadikamalla [29].…”

Section: Introductionmentioning

confidence: 99%

Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution

et al. 2015

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Failure of a component in a composite dynamic system often induces a higher load on surviving components, and increases the hazard rate. Statistical inferential procedures on composite dynamic systems are developed here based on a Burr type-XII distribution with a power-trend hazard rate function. Point estimates of the Burr type-XII parameters, and interval estimates of the baseline survival function are obtained based on the maximum-likelihood estimates, and the Fisher information matrix. A test procedure is presented for examining the relationship between the hazard rate function and the number of failed components. The performance of the proposed method is then evaluated by means of an extensive Monte Carlo simulation study. An example is finally presented for illustrative purpose.Index Terms-Generalized likelihood ratio test, log-likelihood function, observed Fisher information, sequential order statistics.

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Parameter estimation and prediction of order statistics for the Burr Type XII distribution with Type II censoring

Cited by 33 publications

References 18 publications

Model Selection Based on Tracking Interval under Unified Hybrid Censored Samples

Model Selection Based on Tracking Interval under Unified Hybrid Censored Samples

Bayesian Inference of δ = P(X < Y) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples

Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution

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