APPROXIMATE BAYES ESTIMATION OF THE WEIBULL DISTRIBUTION UNDER WEIGHTED LINEX LOSS FUNCTION

In this paper, we developed linear exponential (LINEX) loss function by emerging weights to produce weighted linear exponential (WLINEX) loss function. Then we utilized WLINEX to derive scale parameter and reliability function of the Weibull distribution based on record values when the shape parameter is known. After, we estimated scale parameter and reliability function of Weibull distribution by using maximum likelihood (ML) estimation and by several Bayes estimations. The Bayes estimates were obtained with respect to symmetric loss function (squared error loss (SEL)), asymmetric loss function (LINEX) and asymmetric loss function (WLINEX). The ML and the different Bayes estimates are compared via a Monte Carlo simulation study. The result of simulation mentioned that the proposed WLINEX loss function is promising and can be used in real environment especially at the case of underestimate where it revealed better performance than LINEX loss function for estimating scale parameter.

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Bayes Estimation Based on Joint Progressive Type II Censored Data Under LINEX Loss Function

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918.2012.683921 ◽

2013 ◽

pp. 130102064423005 ◽

Cited By ~ 3

Author(s):

Mahdi Doostparast ◽

Mohammad Vali Ahmadi ◽

Jafar Ahmadi

Keyword(s):

Censored Data ◽

Loss Function ◽

Bayes Estimation ◽

Type Ii ◽

Linex Loss Function ◽

Linex Loss ◽

Progressive Type ◽

Type Ii Censored Data

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

Calcutta Statistical Association Bulletin ◽

10.1177/0008068317696574 ◽

2017 ◽

Vol 69 (1) ◽

pp. 87-102 ◽

Cited By ~ 1

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.

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