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 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 Estimation of Scale Parameter of Weibull-Lomax distribution via Bayesian Approach

2021 ◽  
Vol 09 (05) ◽  
Author(s):  
Arun Kumar Rao, ◽  
Keyword(s):  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Scale Parameter ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Lomax Distribution ◽  
Squared Error

In this paper, the Weibull-Lomax 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 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 Parameter Estimation of Length Biased Weighted Frechet Distribution via Bayesian Approach

2021 ◽  
pp. 42-51
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey
Keyword(s):  
Parameter Estimation ◽  
Bayesian Analysis ◽  
Bayesian Approach ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Fréchet Distribution ◽  
Squared Error ◽  
Frechet Distribution

In this paper, length-biased weighted Frechet 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 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.

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 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.

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