Bayes estimators of the lifetime parameters in the compound Rayleigh distribution using segmented loss functions

2013 ◽  
Author(s):  
Paul Mostert ◽  
A Bekker ◽  
JJJ Roux
Keyword(s):  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Compound Rayleigh Distribution

scholarly journals Bayesian Estimation of the Parameter of the p-Dimensional Size-Biased Rayleigh Distribution

2017 ◽  
Vol 56 (1) ◽  
pp. 88-91
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey ◽  
Kusum Lata Singh
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Bayesian Estimation ◽  
Density Function ◽  
Rayleigh Distribution ◽  
Survival Model ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Hazard Functions ◽  
Squared Error

In this paper, we have derived the probability density function of the size-biased p-dimensional Rayleigh distribution and studied its properties. Its suitability as a survival model has been discussed by obtaining its survival and hazard functions. We also discussed Bayesian estimation of the parameter of the size-biased p-dimensional Rayleigh distribution. Bayes estimators have been obtained by taking quasi-prior. The loss functions used are squared error and precautionary.

scholarly journals Bayesian Estimation of Exponentiated Inverse Rayleigh Distribution

2021 ◽  
Vol 9 (03) ◽  
pp. 321-328
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Estimation ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Squared Error

In this paper, exponentiated inverse Rayleigh 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 Bayes Estimators of Exponentiated Inverse Rayleigh Distribution using Lindleys Approximation

2021 ◽  
pp. 60-71
Author(s):  
Bashiru Omeiza Sule ◽  
Taiwo Mobolaji Adegoke ◽  
Kafayat Tolani Uthman
Keyword(s):  
Loss Function ◽  
Posterior Distribution ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Shape Parameters ◽  
True Parameter ◽  
Squared Error Loss Function ◽  
Scale Parameters

In this paper, Bayes estimators of the unknown shape and scale parameters of the Exponentiated Inverse Rayleigh Distribution (EIRD) have been derived using both the frequentist and bayesian methods. The Bayes theorem was adopted to obtain the posterior distribution of the shape and scale parameters of an Exponentiated Inverse Rayleigh Distribution (EIRD) using both conjugate and non-conjugate prior distribution under different loss functions (such as Entropy Loss Function, Linex Loss Function and Scale Invariant Squared Error Loss Function). The posterior distribution derived for both shape and scale parameters are intractable and a Lindley approximation was adopted to obtain the parameters of interest. The loss function were employed to obtain the estimates for both scale and shape parameters with an assumption that the both scale and shape parameters are unknown and independent. Also the Bayes estimate for the simulated datasets and real life datasets were obtained. The Bayes estimates obtained under dierent loss functions are close to the true parameter value of the shape and scale parameters. The estimators are then compared in terms of their Mean Square Error (MSE) using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

Estimations and Prediction for the Compound Rayleigh Distribution Based on Upper Record Values

2018 ◽  
Vol 15 (2) ◽  
pp. 711-718 ◽  
Author(s):  
M. M. Badr
Keyword(s):  
Prediction Interval ◽  
Record Values ◽  
Rayleigh Distribution ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Upper Record Values ◽  
Upper Record ◽  
Two Parameters ◽  
Compound Rayleigh Distribution

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on upper record values. We have derived the maximum likelihood (ML) and Bayesian estimators for the unknown two parameters, as well as the reliability and hazard functions. We obtained Bayes estimators on the basis of the symmetric (squared error) and asymmetric (linear exponential (LINEX) and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Furthermore, Bayesian prediction interval of the future upper record values are discussed and obtained. Finally, estimation of the parameters, practical examples of real record values and simulated record values are given to illustrate the theoretical results of prediction interval.

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 A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

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