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.

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 Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Kamaljit Kaur ◽  
Sangeeta Arora ◽  
Kalpana K. Mahajan
Keyword(s):  
Loss Function ◽  
Pareto Distribution ◽  
Loss Functions ◽  
Conjugate Prior ◽  
Jeffreys Prior ◽  
Linex Loss Function ◽  
Poverty Measure ◽  
Noninformative Priors ◽  
Simulation Techniques ◽  
Linex Loss

Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

scholarly journals Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution

2018 ◽  
Vol 48 (1) ◽  
pp. 38-55
Author(s):  
M. S. Panwar ◽  
Sanjeev K Tomer
Keyword(s):  
Bayesian Analysis ◽  
Real Data ◽  
Type I ◽  
Lifetime Data ◽  
Maxwell Distribution ◽  
Data Set ◽  
Squared Error ◽  
Robust Bayesian Analysis ◽  
Linex Loss ◽  
Mean Lifetime

In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell distribution assuming an $\varepsilon$-contamination class of prior distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.

scholarly journals E-Bayesian and Bayesian Estimation for the Lomax Distribution under Weighted Composite LINEX Loss Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Afrah Al-Bossly
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Shape Parameter ◽  
Likelihood Estimation ◽  
Loss Functions ◽  
Bayesian Estimator ◽  
Linex Loss Function ◽  
Lomax Distribution ◽  
Linex Loss ◽  
Asymmetric Loss Function

The main contribution of this work is the development of a compound LINEX loss function (CLLF) to estimate the shape parameter of the Lomax distribution (LD). The weights are merged into the CLLF to generate a new loss function called the weighted compound LINEX loss function (WCLLF). Then, the WCLLF is used to estimate the LD shape parameter through Bayesian and expected Bayesian (E-Bayesian) estimation. Subsequently, we discuss six different types of loss functions, including square error loss function (SELF), LINEX loss function (LLF), asymmetric loss function (ASLF), entropy loss function (ENLF), CLLF, and WCLLF. In addition, in order to check the performance of the proposed loss function, the Bayesian estimator of WCLLF and the E-Bayesian estimator of WCLLF are used, by performing Monte Carlo simulations. The Bayesian and expected Bayesian by using the proposed loss function is compared with other methods, including maximum likelihood estimation (MLE) and Bayesian and E-Bayesian estimators under different loss functions. The simulation results show that the Bayes estimator according to WCLLF and the E-Bayesian estimator according to WCLLF proposed in this work have the best performance in estimating the shape parameters based on the least mean averaged squared error.

scholarly journals The Comparison Between the MLE and Standard Bayes Estimators of the Reliability Function of Exponential Distribution

2019 ◽  
Vol 32 (1) ◽  
pp. 103
Author(s):  
Mohammed Jamel Ali ◽  
Hazim Mansoor Gorgees
Keyword(s):  
Loss Function ◽  
Reliability Function ◽  
Loss Functions ◽  
Mean Square ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Monte Carlo Simulation Technique ◽  
Error Loss ◽  
Squared Error ◽  
The One

     In this paper, a Monte Carlo Simulation technique is used to compare the performance of MLE and the standard Bayes estimators of the reliability function of the one parameter exponential distribution.Two types of loss functions are adopted, namely, squared error  loss function (SELF) and modified square error loss function (MSELF) with informative and non- informative prior. The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators .

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 The Comparison Between Standard Bayes Estimators of the Reliability Function of Exponential Distribution

2018 ◽  
Vol 31 (3) ◽  
pp. 135 ◽  
Author(s):  
Mohammed Jamel Ali ◽  
Hazim Mansoor Gorgees ◽  
Adel Abdul Kadhim Hussein
Keyword(s):  
Exponential Distribution ◽  
Loss Function ◽  
Reliability Function ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Monte Carlo Simulation Technique ◽  
Error Loss ◽  
Squared Error ◽  
The One

   In this paper, a Monte Carlo Simulation technique is used to compare the performance of the standard Bayes estimators of the reliability function of the one parameter exponential distribution .Three types of loss functions are adopted, namely, squared error  loss function (SELF) ,Precautionary error loss function (PELF) andlinear exponential error  loss function(LINEX) with informative and non- informative prior .The criterion integrated mean square error (IMSE) is employed to assess the performance of such estimators

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