Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

Angali, Kambiz Ahmadi; Latifi, Seyed Mahmoud; Hanagal, David D.

doi:10.1080/03610918.2012.697963

Cited by 6 publications

(7 citation statements)

References 14 publications

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“…ey obtained posterior mode using gamma Dirichlet distribution as prior distribution. Angali et al [22] considered Bayesian estimation for BVE using gamma prior.…”

Section: Using Maximum Likelihood Approachmentioning

confidence: 99%

Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

Aly

Abuelamayem

2020

Mathematical Problems in Engineering

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Industrial revolution leads to the manufacturing of multicomponent products; to guarantee the sufficiency of the product and consumer satisfaction, the producer has to study the lifetime of the products. This leads to the use of bivariate and multivariate lifetime distributions in reliability engineering. The most popular and applicable is Marshall–Olkin family of distributions. In this paper, a new bivariate lifetime distribution which is the bivariate inverted Kumaraswamy (BIK) distribution is found and its properties are illustrated. Estimation using both maximum likelihood and Bayesian approaches is accomplished. Using different selection criteria, it is found that BIK provides the best performance compared with other bivariate distributions like bivariate exponential and bivariate inverse Weibull distributions. As a generalization, the multivariate inverted Kumaraswamy (MIK) distribution is derived. Few studies have been conducted on the multivariate Marshall–Olkin lifetime distributions. To the best of our knowledge, none of them handle estimation process. In this paper, we developed an algorithm to show how to estimate the unknown parameters of MIK using both maximum likelihood and Bayesian approaches. This algorithm could be applied in estimating other Marshall–Olkin multivariate lifetime distributions.

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“…ey obtained posterior mode using gamma Dirichlet distribution as prior distribution. Angali et al [22] considered Bayesian estimation for BVE using gamma prior.…”

Section: Using Maximum Likelihood Approachmentioning

confidence: 99%

Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

Aly

Abuelamayem

2020

Mathematical Problems in Engineering

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“…The strengths of the components, are independently and identically distributed random variables with distribution function F(.). Then the reliability of the system is given by the equation (1). Now, we assume that (X 1 , Y 1 ), (X 2 , Y 2 ), ... , (X k , Y k ) be independently and identically distributed random variables having BGR (λ 1 , λ 2 , λ 3, γ) distributed and T is a random variable from GR (δ, , γ) distribution.…”

Section: System Reliabilitymentioning

confidence: 99%

“…A simulation study is conducted to compare the performance of the proposed estimators of system reliability for different sample sizes. 100000 random samples of size n, m, m x , m y, r x and r y were generated for the stress and strength populations, when (λ, δ, γ) = (4.5, 0.8, 1), (8, 0.3, 1.5) and (1.07, 1, 1) with the true values of stress-strength reliability for (s, k) = (1,3)…”

Section: Simulation Studymentioning

confidence: 99%

“…Estimation of Reliability for stress-strength model, when X and Y have bivariate exponential distribution was considered by Awed et al, (1981), Jana(1994), Hanagal (1995), while Hanagal (1997) considered the estimation of the reliability when (X, Y ) follow bivariate pareto distribution. Angali et al (2014) considered Bayesian estimation for four parameter bivariate exponential distribution under different loss functions. Hanagal (2003), estimated system reliability, R = P(X k+1 < min(X 1 ,...,X k )) under the assumption that strengths of the k components (X 1 ,...,X k ) subjected to a common stress X k+1 , when (X 1 ,..,X k+1 ) follow (k +1) statistically independent gamma or Weibull or Pareto distributions.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Multicomponent System Reliability for a Bivariate Generalized Rayleigh Distribution

Pandit¹,

Shubhashree²

2019

IJCTS

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The study of a multicompnent system with k identical components which are independent to each other is considered in the present work. The components of the system have series structure with two dependent elements that are exposed to a common random stress. Here, strength vectors follow bivariate generalized Rayleigh distribution and a common random stress follow generalized Rayleigh distribution. The s-out-of-k system is said to function if atleast s out of k(1 ≤ s ≤ k) strength variables exceed the random stress. The estimation of system reliability is studied using maximum likelihood and Bayesian approaches. The maximum likelihood estimates are derived under simple random sampling and ranked set sampling schemes. The approximate Bayes estimates for system reliability are obtained using Lindley's approximation technique. Simulation study is conducted to study the performance of the estimators of reliability using mean squares error criteria.

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“…Wong [4] obtained confidence intervals for P(X > Y) when the underlying distribution is generalized Pareto. Angali et al [5] considered Bayesian estimators of reliability for four parameter of bivariate exponential distribution under different loss functions.…”

Section: Introductionmentioning

confidence: 99%

Reliability Estimation in Multicomponent Stress-strength Model based on Generalized Pareto Distribution

Pandit¹,

Joshi²

2018

AJAMS

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The paper deals with the estimation of multicomponent system reliability where the system has k components with their strengths X 1 , X 2 , … X k being independently and identically distributed random variables and each component is experiencing a random stress Y. The s-out-of-k system is said to function if atleast s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The reliability of such a system is derived when both strength and stress variables follow generalized Pareto distribution. The system reliability is estimated using maximum likelihood and Bayesian approaches. The maximum likelihood estimators are derived under both simple random sampling and ranked set sampling schemes. Lindley's approximation technique is used to get approximate Bayes estimators. The reliability estimators obtained from both the methods are compared by using mean squares error criteria and real data analysis is carried out to illustrate the procedure.

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Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

Cited by 6 publications

References 14 publications

Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

Multivariate Inverted Kumaraswamy Distribution: Derivation and Estimation

Estimation of Multicomponent System Reliability for a Bivariate Generalized Rayleigh Distribution

Reliability Estimation in Multicomponent Stress-strength Model based on Generalized Pareto Distribution

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