Bayes Estimation of Augmenting Gamma Strength Reliability of a System under Non-informative Prior Distributions

2017 ◽  
Vol 69 (1) ◽  
pp. 87-102 ◽  
Author(s):  
N. Chandra ◽  
V.K. Rathaur
Keyword(s):  
Loss Function ◽  
Bayes Estimation ◽  
Linex Loss Function ◽  
Squared Error Loss Function ◽  
Squared Error ◽  
Linex Loss ◽  
Augmentation Strategy ◽  
Mean Square Errors ◽  
Informative Prior Distributions ◽  
Common Shape

In this article, Bayes estimation of system’s augmented strength reliability is studied under squared-error loss function (SELF) and LINEX loss function (LLF) for the generalized case of augmentation strategy plan (ASP). ASP is helpful in enhancing the strength reliability of weaker system/equipment. It is assumed that the stress (usual) and augmented strength follow a gamma distribution with common shape [Formula: see text] and scale [Formula: see text] parameters. A simulation study is performed for the comparisons of Bayes estimators of augmented strength reliability for non-informative types of prior (uniform and Jeffrey’s priors) with maximum likelihood estimators on the basis of their mean square errors and the absolute biases by simulating 1,000 Monte Carlo samples. The proposed methods are compared by analysing real and simulated datasets for illustration purpose.

scholarly journals Bayesian Estimation of Weighted Inverse Maxwell Distribution under Different Loss Functions

2021 ◽  
pp. 189-203
Author(s):  
Aijaz Ahmad ◽  
Rajnee Tripathi
Keyword(s):  
Loss Function ◽  
Loss Functions ◽  
Posterior Distributions ◽  
Maxwell Distribution ◽  
Linex Loss Function ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Bayesian Techniques ◽  
Squared Error ◽  
Linex Loss

In this study, the shape parameter of the weighted Inverse Maxwell distribution is estimated by employing Bayesian techniques. To produce posterior distributions, the extended Jeffery's prior and the Erlang prior are utilised. The estimators are derived from the squared error loss function, the entropy loss function, the precautionary loss function, and the Linex loss function. Furthermore, an actual data set is studied to assess the effectiveness of various estimators under distinct loss functions.

scholarly journals Estimating the Common Mean of k Normal Populations with Known Variance

2017 ◽  
Vol 6 (4) ◽  
pp. 70
Author(s):  
N. Sanjari Farsipour ◽  
A. Asgharzadeh
Keyword(s):  
Loss Function ◽  
Linex Loss Function ◽  
Common Mean ◽  
Normal Populations ◽  
Squared Error ◽  
Linex Loss ◽  
The Common

Consider the problem of estimating the common mean of knormal populations with known variances. We study the admisibility of the Best linear Risk Unbiased Equivariant (BLRUE)estimator of the common mean of k normalpopulations underthe squared error and LINEX loss function when the variancesare known.

scholarly journals Estimating the Common Mean of k Normal Populations with Known Variance

2016 ◽  
Vol 6 (4) ◽  
pp. 70
Author(s):  
N. Sanjari Farsipour ◽  
A. Asgharzadeh
Keyword(s):  
Loss Function ◽  
Linex Loss Function ◽  
Common Mean ◽  
Normal Populations ◽  
Squared Error ◽  
Linex Loss ◽  
The Common

Consider the problem of estimating the common mean of knormal populations with known variances. We study the admisibility of the Best linear Risk Unbiased Equivariant (BLRUE)estimator of the common mean of k normalpopulations underthe squared error and LINEX loss function when the variancesare known.

scholarly journals Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function

2020 ◽  
Vol 9 (2) ◽  
pp. 38
Author(s):  
Josphat. K. Kinyanjui ◽  
Betty. C. Korir
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Risk Function ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

scholarly journals E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

2015 ◽  
Vol 3 (2) ◽  
pp. 108 ◽  
Author(s):  
Hesham Reyad ◽  
Soha Othman Ahmed
Keyword(s):  
Loss Function ◽  
Shape Parameter ◽  
Quadratic Loss ◽  
Type Ii ◽  
Linex Loss Function ◽  
Censored Samples ◽  
Squared Error ◽  
Linex Loss ◽  
Symmetric Loss ◽  
Bayesian Estimators

<p>This paper seeks to focus on Bayesian and E-Bayesian estimation for the unknown shape parameter of the Gumbel type-II distribution based on type-II censored samples. These estimators are obtained under symmetric loss function [squared error loss (SELF))] and various asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF), Quadratic loss function (QLF) and minimum expected loss function (MELF)]. Comparisons between the E-Bayesian estimators with the associated Bayesian estimators are investigated through a simulation study.</p>

scholarly journals Bayesian and E-Bayesian estimation for the Kumaraswamy distribution based on type-ii censoring

2016 ◽  
Vol 4 (1) ◽  
pp. 10 ◽  
Author(s):  
Hesham Reyad ◽  
Soha Othman Ahmed
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Quadratic Loss ◽  
Type Ii ◽  
Linex Loss Function ◽  
Kumaraswamy Distribution ◽  
Squared Error ◽  
Linex Loss ◽  
Symmetric Loss ◽  
Bayesian Estimators

<p>This paper introduces the Bayesian and E-Bayesian estimation for the shape parameter of the Kumaraswamy distribution based on type-II censored schemes. These estimators are derived under symmetric loss function [squared error loss (SELF))] and three asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF) and Quadratic loss function (QLF)]. Monte Carlo simulation is performed to compare the E-Bayesian estimators with the associated Bayesian estimators in terms of Mean Square Error (MSE).</p>

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