scholarly journals Bayesian Estimation of the Scale Parameter of Inverse Weibull Distribution under the Asymmetric Loss Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Farhad Yahgmaei ◽  
Manoochehr Babanezhad ◽  
Omid S. Moghadam
Keyword(s):  
Weibull Distribution ◽  
Scale Parameter ◽  
Loss Functions ◽  
Simulation Studies ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Risk Functions ◽  
Inverse Weibull Distribution ◽  
The Mean ◽  
Mean Square Errors

This paper proposes different methods of estimating the scale parameter in the inverse Weibull distribution (IWD). Specifically, the maximum likelihood estimator of the scale parameter in IWD is introduced. We then derived the Bayes estimators for the scale parameter in IWD by considering quasi, gamma, and uniform priors distributions under the square error, entropy, and precautionary loss functions. Finally, the different proposed estimators have been compared by the extensive simulation studies in corresponding the mean square errors and the evolution of risk functions.

scholarly journals Reliability estimation and parameter estimation for inverse Weibull distribution under different loss functions

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Asuman Yilmaz ◽  
◽  
Mahmut Kara ◽  
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimators ◽  
Loss Functions ◽  
Estimation Methods ◽  
Mcmc Methods ◽  
Inverse Weibull Distribution ◽  
Mean Square Errors ◽  
Bayesian Estimators

In this paper, the classical and Bayesian estimators of the unknown parameters and the reliability function of the inverse Weibull distribution are considered. The maximum likelihood estimators (MLEs) and modified maximum likelihood estimators (MMLEs) are used in the classical parameter estimation. Bayesian estimators of the parameters are obtained by using symmetric and asymmetric loss functions under informative and non-informative priors. Bayesian computations are derived by using Lindley approximation and Markov chain Monte Carlo (MCMC) methods. The asymptotic confidence intervals are constructed based on the maximum likelihood estimators. The Bayesian credible intervals of the parameters are obtained by using the MCMC method. Furthermore, the performances of these estimation methods are compared concerning their biases and mean square errors through a simulation study. It is seen that the Bayes estimators perform better than the classical estimators. Finally, two real-life examples are given for illustrative purposes.

A SIMPLE ESTIMATOR FOR THE WEIBULL SHAPE PARAMETER

2012 ◽  
Vol 12 (02) ◽  
pp. 395-402 ◽  
Author(s):  
MAHDI TEIMOURI ◽  
SARALEES NADARAJAH
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Closed Form ◽  
Maximum Likelihood Estimator ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Maximum Likelihood Estimators ◽  
Simulation Studies ◽  
Likelihood Estimator

The Weibull distribution is the most popular model for lifetimes. However, the maximum likelihood estimators for the Weibull distribution are not available in closed form. In this note, we derive a simple, consistent, closed form estimator for the Weibull shape parameter. This estimator is independent of the Weibull scale parameter. Simulation studies show that this estimator performs as well as the maximum likelihood estimator.

scholarly journals Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

2021 ◽  
Vol 2021 ◽  
pp. 1-9 ◽  
Author(s):  
Fuad S. Al-Duais
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Likelihood Estimation ◽  
Reliability Function ◽  
Record Values ◽  
Loss Functions ◽  
Squared Error ◽  
Inverse Weibull Distribution ◽  
Mathematical Justification

The main contribution of this work is to develop a linear exponential loss function (LINEX) to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values. We do this by merging a weight into LINEX to produce a new loss function called weighted linear exponential loss function (WLINEX). We then use WLINEX to derive the scale parameter and reliability function of the IWD. Subsequently, we discuss the balanced loss functions for three different types of loss function, which include squared error (SE), LINEX, and WLINEX. The majority of previous scholars determined the weighted balanced coefficients without mathematical justification. One of the main contributions of this work is to utilize nonlinear programming to obtain the optimal values of the weighted coefficients for balanced squared error (BSE), balanced linear exponential (BLINEX), and balanced weighted linear exponential (BWLINEX) loss functions. Furthermore, to examine the performance of the proposed methods—WLINEX and BWLINEX—we conduct a Monte Carlo simulation. The comparison is between the proposed methods and other methods including maximum likelihood estimation, SE loss function, LINEX, BSE, and BLINEX. The results of simulation show that the proposed models BWLINEX and WLINEX in this work have the best performance in estimating scale parameter and reliability, respectively, according to the smallest values of mean SE. This result means that the proposed approach is promising and can be applied in a real environment.

Data Processing with Computation in Bayes Reliability Analysis for Burr Type X Distribution under Different Loss Functions

2014 ◽  
Vol 978 ◽  
pp. 205-208
Author(s):  
Hui Zhou
Keyword(s):  
Prior Distribution ◽  
Unknown Parameter ◽  
Empirical Bayes ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Likelihood Estimator ◽  
Squared Error Loss ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimators

This paper studies the estimation of the parameter of Burr Type X distribution. Maximum likelihood estimator is first derived, and then the Bayes and Empirical Bayes estimators of the unknown parameter are obtained under three loss functions, which are squared error loss, LINEX loss and entropy loss functions. The prior distribution of parmeter used in this paper is Gamma distribution. Finally, a Monte Carlo simulation is given to illustrate the application of these estimators.

scholarly journals Comparative Study of Reliability of Some Antiseptic Soaps; A 3- Parameter Weibull Distribution

2015 ◽  
Vol 1 (01) ◽  
Author(s):  
Olubiyi O. A.
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Weibull Distribution ◽  
Dissolution Time ◽  
Time To Failure ◽  
Likelihood Estimator ◽  
Method Of Maximum Likelihood ◽  
Mean And Variance ◽  
The Mean ◽  
Parameter Case

This study was carried out to estimate the dissolution time of some antiseptic soaps . The lifetime behavior of the antiseptic soaps was also modeled in order to estimate some basic measures and compare their lifetimes. In the analysis of data, the weibull distribution of 3-parameter case was used. The method of maximum likelihood estimator was used in estimating the parameters. The mean and variance time to failure, reliability, Weibull conditional reliability and Weibull reliable life of the products were obtained.

scholarly journals Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Kaisar Ahmad ◽  
S. P. Ahmad ◽  
A. Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Bayesian Approach ◽  
Simulation Study ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
R Software ◽  
Nakagami Distribution

Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.

scholarly journals On Parameters Estimation of Lomax Distribution under General Progressive Censoring

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Bander Al-Zahrani ◽  
Mashail Al-Sobhi
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Parameters Estimation ◽  
Loss Functions ◽  
Mcmc Methods ◽  
Bayes Estimators ◽  
Progressive Censoring ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Study ◽  
Lomax Distribution

We consider the estimation problem of the probability S=P(Y<X) for Lomax distribution based on general progressive censored data. The maximum likelihood estimator and Bayes estimators are obtained using the symmetric and asymmetric balanced loss functions. The Markov chain Monte Carlo (MCMC) methods are used to accomplish some complex calculations. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation study.

scholarly journals Bayesian Modeling of 3-Component Mixture of Exponentiated Inverted Weibull Distribution under Noninformative Prior

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Ammara Nawaz Cheema ◽  
Muhammad Aslam ◽  
Ibrahim M. Almanjahie ◽  
Ishfaq Ahmad
Keyword(s):  
Weibull Distribution ◽  
Research Work ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Bayes Estimators ◽  
Component Mixture ◽  
Type I Censoring ◽  
Censoring Technique ◽  
The Impact

Bayesian study of 3-component mixture modeling of exponentiated inverted Weibull distribution under right type I censoring technique is conducted in this research work. The posterior distribution of the parameters is obtained assuming the noninformative (Jeffreys and uniform) priors. The different loss functions (squared error, quadratic, precautionary, and DeGroot loss function) are used to obtain the Bayes estimators and posterior risks. The performance of the Bayes estimators through posterior risks under the said loss functions is investigated through simulation process. Real data analysis of tensile strength of carbon fiber is also applied for 3 components to conclude the presentation of Bayes estimators. The limiting expressions are also elaborated for Bayes estimators and posterior risks in this study. The impact of some test termination times and sample sizes is reported on Bayes estimators.

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&nbsp; &theta;&nbsp; and shape parameter&nbsp; &beta; (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter,&nbsp;&theta;&nbsp; , 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.

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