On the estimation of stress strength reliability parameter of inverted gamma distribution

Iranmanesh, Anis; Vajargah, Kianoosh Fathi; Hasanzadeh, Mahdi

doi:10.1007/s40096-018-0246-4

Cited by 16 publications

(13 citation statements)

References 14 publications

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“…To assess the performance of the bootstrap confidence interval we reported the confidence length and the coverage percentage. We considered different sample sizes say; (n, m) = (5, 5), (5, 10), (10, 5), (10, 10), (10,15), (15,10), (20,20), (30,30). Since the value of R is independent of β without loss of generality we kept it constant at β = 1.0.…”

Section: Simulation Studymentioning

confidence: 99%

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Inference on P[Y < X] for Geometric Extreme Exponential Distribution

Pakyari¹

2021

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Geometric Extreme Exponential Distribution (GEE) is one of the statistical models that can be useful in fitting and describing lifetime data. In this paper, the problem of estimation of the reliability R = P (Y < X) when X and Y are independent GEE random variables with common scale parameter but different shape parameters has been considered. The probability R = P (Y < X) is also known as stress-strength reliability parameter and demonstrates the case where a component has stress X and is subjected to strength Y . The reliability R = P (Y < X) has applications in engineering, finance and biomedical sciences. We present the maximum likelihood estimator of R and study its asymptotic behavior. We first study the asymptotic distribution of the maximum likelihood estimators of the GEE parameters. We prove that the maximum likelihood estimators and so the reliability R have asymptotic normal distribution. A bootstrap confidence interval for R is also presented. Monte Carlo simulations are performed to assess he performance of the proposed estimation method and validity of the confidence interval. We found that the performance of the maximum likelihood estimator and also the bootstrap confidence interval is satisfactory even for small sample sizes. Analysis of a dataset has been given for illustrative purposes.

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Section: Simulation Studymentioning

confidence: 99%

“…Reference [18] collects and analysis different stress-strength models. See also [19], [15], [5,6], [7], [16] and [33].…”

Section: Introductionmentioning

confidence: 99%

Inference on P[Y < X] for Geometric Extreme Exponential Distribution

Pakyari¹

2021

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“…Glen (2011) presented properties of the inverse gamma distribution and how it can be used as a survival distribution. Iranmanesh, Vajargah, and Hasanzadeh (2018) considered the likelihood estimation of stress-strength reliability from the generalized exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

Reparameterized inverse gamma regression models with varying precision

Bourguignon

Gallardo

2020

Statistica Neerlandica

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In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model.

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“…It is often assumed that X and Y are independent random variables and that they belong to the same family of probability distributions. Iranmanesh et al (2018) dealt with the estimation of R when the random variables have inverted gamma distributions. Wang et al (2018) developed inferential procedures for the stress-strength probability when the random variables are generalized exponential.…”

Section: Introductionmentioning

confidence: 99%

Stress–strength reliability models involving generalized gamma and Weibull distributions

Nojosa

Rathie

2020

IJQRM

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PurposeThis paper deals with the estimation of the stress–strength reliability R = P(X < Y), when X and Y follow (1) independent generalized gamma (GG) distributions with only a common shape parameter and (2) independent Weibull random variables with arbitrary scale and shape parameters and generalize the proposal from Kundu and Gupta (2006), Kundu and Raqab (2009) and Ali et al. (2012).Design/methodology/approachFirst, a closed form expression for R is derived under the conditions (1) and (2). Next, sufficient conditions are given for the convergence of the infinite series expansions used to calculate the value of R in case (2). The models GG and Weibull are fitted by maximum likelihood using Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method. Confidence intervals and standard errors are calculated using bootstrap. For illustration purpose, two real data sets are analyzed and the results are compared with the existing recent results available in the literature.FindingsThe proposed approaches improve the estimation of the R by not using transformations in the data and flexibilize the modeling with Weibull distributions with arbitrary scale and shape parameters.Originality/valueThe proposals of the paper eliminate the misestimation of R caused by subtracting a constant value from the data (Kundu and Raqab, 2009) and treat the estimation of R in a more adequate way by using the Weibull distributions without restrictions in the parameters. The two cases covered generalize a number of distributions and unify a number of stress–strength probability P(X < Y) results available in the literature.

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On the estimation of stress strength reliability parameter of inverted gamma distribution

Cited by 16 publications

References 14 publications

Inference on P[Y < X] for Geometric Extreme Exponential Distribution

Inference on P[Y < X] for Geometric Extreme Exponential Distribution

Reparameterized inverse gamma regression models with varying precision

Stress–strength reliability models involving generalized gamma and Weibull distributions

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