Estimation of the Parameters of the Birnbaum–Saunders Distribution

From, Steven G.; Li, Linxiong

doi:10.1080/03610920600853563

Cited by 26 publications

(18 citation statements)

References 7 publications

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“…Desmond [9] also strengthened the physical justification for the use of this distribution by relaxing the assumptions made originally by Birnbaum and Saunders [4]. Some recent work on the BS distribution can be found in Balakrishnan et al [2], Chang and Tang [7,8], Dupuis and Mills [10], From and Li [11],…”

Section: Introductionmentioning

confidence: 99%

On the hazard function of Birnbaum–Saunders distribution and associated inference

Kundu

Kannan

Balakrishnan

2008

Computational Statistics & Data Analysis

123

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In this paper, we discuss the shape of the hazard function of Birnbaum-Saunders distribution. Specifically, we establish that the hazard function of Birnbaum-Saunders distribution is an upside down function for all values of the shape parameter. In reliability and survival analysis, as it is often of interest to determine the point at which the hazard function reaches its maximum, we propose different estimators of that point and evaluate their performance using Monte Carlo simulations. Next, we analyze a data set and illustrate all the inferential methods developed here and finally make some concluding remarks.

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Section: Introductionmentioning

confidence: 99%

On the hazard function of Birnbaum–Saunders distribution and associated inference

Kundu

Kannan

Balakrishnan

2008

Computational Statistics & Data Analysis

123

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“…It can model the failure time of fatigue process under the assumption that the failure is due to the development and growth of a dominant crack. Some recent works on the parameter inference of the BS distribution can be seen in From and Li [12], Kundu et al [13], Lemonte et al [14], Ng et al [15,16], Owen [17], and Xie and Wei [18]. Balakrishnan et al [5] proposed a single sampling plan for a generalized BS distribution, where the parameters were determined by considering only the consumer's risk.…”

Section: The Bs Distributionmentioning

confidence: 98%

New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions

Aslam

Jun

Ahmad

2011

Journal of Statistical Computation and Simulation

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In this paper, we consider the Birnbaum-Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.

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“…, n. We shall denote the jackknife maximum likelihood estimators asᾱ Ng JMLE andβ Ng JMLE ; the jackkinife moment estimator arē α Ng JMME andβ Ng JMME . From and Li (2006) also proposed alternative estimators for the two parameters that index the Birnbaum-Saunders distribution. For instance, they proposed using…”

Section: Alternative Inference Strategiesmentioning

confidence: 99%

“…, α(n)). From and Li (2006) have also proposed yet another estimator for (α, β). Let 0 < λ < 0.5, and let n 1 = nλ + 1 and n 2 = n(1 − λ), to the nearest integer.…”

Section: Alternative Inference Strategiesmentioning

confidence: 99%

“…We shall now compare the small sample behavior of our adjusted profile maximum likelihood estimators of α to those proposed by Ng, Kundu and Balakrishnan (2003) and From and Li (2006), which are described in Section 4. The number of Monte Carlo replications is, as before, 10,000, the true values of α are 0.5 and 1.0, and n = 10.…”

Section: Additional Numerical Evidence: Comparison With Alternative Ementioning

confidence: 99%

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On Birnbaum–Saunders inference

Cysneiros

Cribari‐Neto

Araújo

2008

Computational Statistics & Data Analysis

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The Birnbaum-Saunders distribution, also known as the fatigue-life distribution, is frequently used in reliability studies. We obtain adjustments to the Birnbaum-Saunders profile likelihood function. The modified versions of the likelihood function were obtained for both the shape and scale parameters, i.e., we take the shape parameter to be of interest and the scale parameter to be of nuisance, and then consider the situation in which the interest lies in performing inference on the scale parameter with the shape parameter entering the modeling in nuisance fashion. Modified profile maximum likelihood estimators are obtained by maximizing the corresponding adjusted likelihood functions. We present numerical evidence on the finite sample behavior of the different estimators and associated likelihood ratio tests. The results favor the adjusted estimators and tests we propose. A novel aspect of the profile likelihood adjustments obtained in this paper is that they yield improved point estimators and tests. The two profile likelihood adjustments work well when inference is made on the shape parameter, and one of them displays superior behavior when it comes to performing hypothesis testing inference on the scale parameter. Two empirical applications are briefly presented.

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Estimation of the Parameters of the Birnbaum–Saunders Distribution

Cited by 26 publications

References 7 publications

On the hazard function of Birnbaum–Saunders distribution and associated inference

On the hazard function of Birnbaum–Saunders distribution and associated inference

New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions

On Birnbaum–Saunders inference

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