Estimation of Pr(Y &lt; X) for the two-parameter generalized exponential records

Asgharzadeh, A.; Valiollahi, Reza; Raqab, Mohammad Z.

doi:10.1080/03610918.2014.964046

Cited by 27 publications

(14 citation statements)

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“…Instead of minimizing (11), the estimatesb 1 LSE ;b 2 LSE andâ LSE can be obtained by solving the following three equations simultaneously…”

Section: Least Square and Weighted Least Square Estimationmentioning

confidence: 99%

“…[5] considered the estimation of R, where X and Y are two independent generalized Pareto distributions. In recent years, a many works have been done on the problem of estimating R of some distributions; See for example, [6][7][8][9][10][11][12][13][14] and [15]. These studies have actually considered the maximum likelihood and Bayesian estimation methods under different life testing schemes for various distributions.…”

Section: Introductionmentioning

confidence: 99%

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On estimation procedures of stress-strength reliability for Weibull distribution with application

2020

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For the first time, ten frequentist estimation methods are considered on stress-strength reliability R = P(Y < X) when X and Y are two independent Weibull distributions with the same shape parameter. The start point to estimate the parameter R is the maximum likelihood method. Other than the maximum likelihood method, a nine frequentist estimation methods are used to estimate R, namely: least square, weighted least square, percentile, maximum product of spacing, minimum spacing absolute distance, minimum spacing absolute-log distance, method of Cramé r-von Mises, Anderson-Darling and Right-tail Anderson-Darling. We also consider two parametric bootstrap confidence intervals of R. We compare the efficiency of the different proposed estimators by conducting an extensive Mont Carlo simulation study. The performance and the finite sample properties of the different estimators are compared in terms of relative biases and relative mean squared errors. The Mont Carlo simulation study revels that the percentile and maximum product of spacing methods are highly competitive with the other methods for small and large sample sizes. To show the applicability and the importance of the proposed estimators, we analyze one real data set.

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“…Instead of minimizing (11), the estimatesb 1 LSE ;b 2 LSE andâ LSE can be obtained by solving the following three equations simultaneously…”

Section: Least Square and Weighted Least Square Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On estimation procedures of stress-strength reliability for Weibull distribution with application

2020

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“…In [18], the authors assumed that these data followed the two-parameter GED(4.1016,0.0062). Therefore, when all elements of this dataset are multiplied by 0.0062, we have a dataset that follows the one parameter GE(4.1016); see [10].…”

Section: An Illustrative Examplesmentioning

confidence: 99%

Bayesian Prediction of Order Statistics Based on k-Record Values from a Generalized Exponential Distribution

Vidović

2019

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“…When the X and Y are independent and follow the Burr Type III, X and XII, generalized exponential, Weibull, Gompertz, Kumaraswamy and Levy distributions, the estimation of R based on a random sample were studied by Mokhlis [31], Ahmad et al [1], Awad and Gharraf [9], Kundu Gupta [25,26], Saraçoglu et al [41], Nadar et al [32] and Najarzadegan et al [36], respectively. When the X and Y are independent and follow one and two parameters generalized exponential, Weibull, exponentiated gumbel, Kumaraswamy, one and two parameters exponential and Burr Type X distributions, the classical and Bayesian estimates of R based on records were considered by Baklizi [10], Asgharzadeh et al [7], Baklizi [11], Tavirdizade [43], Nadar and Kızılaslan [33], Baklizi [12] and Tavirdizade and Garehchobogh [44], respectively. The Burr Type XII distribution was introduced by Burr [16].…”

Section: Introductionmentioning

confidence: 99%

“…(3.2) and(3.4). The point and interval estimates are computed for R = 0.25, 0.33, 0.50, 0, 70, 0.90 and 0.92 when (β 1 , β 2 ) = (2, 6),(2,4),(2,2),(7,3),(18,2) and(23,2), respectively. FromTable 4, the ERs of all estimates decrease as the sample sizes increase in all cases, as expected.The Bayes estimates under the SE loss function with their corresponding ERs are close to their response in the ML case.…”

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confidence: 99%

Statistical inference of P(X Y ) for the Burr Type XII distribution based on records

Kızılaslan¹,

Nadar²

2015

HJMS

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In this paper, the maximum likelihood and Bayesian approaches have been used to obtain the estimates of the stress-strength reliability R = P (X < Y) based on upper record values for the two-parameter Burr Type XII distribution. A necessary and sufficient condition is studied for the existence and uniqueness of the maximum likelihood estimates of the parameters. When the first shape parameter of X and Y is common and unknown, the maximum likelihood (ML) estimate and asymptotic confidence interval of R are obtained. In this case, the Bayes estimate of R has been developed by using Lindley's approximation and the Markov Chain Monte Carlo (MCMC) method due to lack of explicit forms under the squared error (SE) and linear-exponential (LINEX) loss functions for informative prior. The MCMC method has been also used to construct the highest posterior density (HPD) credible interval. When the first shape parameter of X and Y is common and known, the ML, uniformly minimum variance unbiased (UMVU) and Bayes estimates, Bayesian and HPD credible as well as exact and approximate intervals of R are obtained. The comparison of the derived estimates is carried out by using Monte Carlo simulations. Two real life data sets are analysed for the illustration purposes.

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Estimation of Pr(Y < X) for the two-parameter generalized exponential records

Cited by 27 publications

References 1 publication

On estimation procedures of stress-strength reliability for Weibull distribution with application

On estimation procedures of stress-strength reliability for Weibull distribution with application

Bayesian Prediction of Order Statistics Based on k-Record Values from a Generalized Exponential Distribution

Statistical inference of P(X Y ) for the Burr Type XII distribution based on records

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