scholarly journals Bayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions

2020 ◽  
Author(s):  
Gaurav Shukla ◽  
Umesh Chandra ◽  
Vinod Kumar
Keyword(s):  
Shape Parameter ◽  
Pareto Distribution ◽  
Risk Function ◽  
Simulated Data ◽  
Reliability Function ◽  
Minimum Variance ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Data Set

In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

scholarly journals Bayes Estimation of Shape Parameter of Length Biased Weibull Distribution

2021 ◽  
Vol 5 (1) ◽  
pp. 28
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Shape Parameter ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Squared Error

In this paper, length biased Weibull distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Bayes Estimation of a Two-Parameter Geometric Distribution under Multiply Type II Censoring

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
J. B. Shah ◽  
M. N. Patel
Keyword(s):  
Geometric Distribution ◽  
Correct Choice ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Type Ii ◽  
Expected Loss ◽  
Bayes Estimators ◽  
Linex Loss ◽  
Type Ii Censored Data ◽  
Two Parameter

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

scholarly journals Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Navid Feroz
Keyword(s):  
Bayesian Inference ◽  
Loss Function ◽  
Simulation Study ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Bayes Estimators ◽  
Type Viii ◽  
Censored Samples ◽  
Made In

This paper is concerned with estimation of the parameter of Burr type VIII distribution under a Bayesian framework using censored samples. The Bayes estimators and associated risks have been derived under the assumption of five priors and three loss functions. The comparison among the performance of different estimators has been made in terms of posterior risks. A simulation study has been conducted in order to assess and compare the performance of different estimators. The study proposes the use of inverse Levy prior based on quadratic loss function for Bayes estimation of the said parameter.

scholarly journals Bayes Estimation of Change Point in Discrete Maxwell Distribution

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Mayuri Pandya ◽  
Hardik Pandya
Keyword(s):  
Change Point ◽  
Prior Information ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Maxwell Distribution ◽  
Bayes Estimators ◽  
Asymmetric Loss ◽  
Bayes Estimates

A sequence of independent lifetimes X1,…,Xm,Xm+1,…,Xn was observed from Maxwell distribution with reliability r1(t) at time t but later, it was found that there was a change in the system at some point of time m and it is reflected in the sequence after Xm by change in reliability r2(t) at time t. The Bayes estimators of m, θ1, θ2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

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 Bayesian Analysis of a Shape Parameter of the Weibull-Frechet Distribution

2018 ◽  
pp. 1-19
Author(s):  
Terna Godfrey Ieren ◽  
Angela Unna Chukwu
Keyword(s):  
Loss Function ◽  
Shape Parameter ◽  
Real Life ◽  
Loss Functions ◽  
Quadratic Loss ◽  
Bayes Estimators ◽  
Informative Priors ◽  
Fréchet Distribution ◽  
Minimum Bayes Risk ◽  
Frechet Distribution

In this paper, we estimate a shape parameter of the Weibull-Frechet distribution by considering the Bayesian approach under two non-informative priors using three different loss functions. We derive the corresponding posterior distributions for the shape parameter of the Weibull-Frechet distribution assuming that the other three parameters are known. The Bayes estimators and associated posterior               risks have also been derived using the three different loss functions. The performance of the Bayes estimators are evaluated and compared using a comprehensive simulation study and a real life application to find out the combination of a loss function and a prior having the minimum Bayes risk and hence producing the best results. In conclusion, this study reveals that in order to estimate the parameter in question, we should use quadratic loss function under either of the two non-informative priors used in this study.  

The Best Estimators of Quantiles and the Three Means of the Pareto Distribution

1986 ◽  
Vol 35 (3-4) ◽  
pp. 111-122
Author(s):  
T. S. K. Moothathu
Keyword(s):  
Shape Parameter ◽  
Pareto Distribution ◽  
Geometric Mean ◽  
Minimum Variance ◽  
Confluent Hypergeometric Function ◽  
Kummer’S Function ◽  
Function Of Two Variables ◽  
Best Estimator ◽  
Strongly Consistent ◽  
Appell Function

In this paper we develop the uniformly minimum variance unbiased (best) estimators of the quantiles, mean, geometric mean and harmonic mean of the Pareto distribuion in the case when both the shape parameter a and the scale parameter k are unknown and in cases when one of them alone is unknown. The best estimates are in terms of the Bessel Function o F1 and Kummer's function 1 F1. The variance of the best estimator are found out, which are in terms of F2 , the Appell function of second kind and ψ2 , a confluent hypergeometric function of two variables. Further we prove that every best estimator of this paper is strongly consistent.

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