Bayesian Estimation of the Shape Parameter of Generalized Rayleigh Distribution Under Symmetric and Asymmetric Loss Functions

Description

– Bayesian Estimation of the Shape Parameter of Generalized Rayleigh Distribution Under Symmetric and Asymmetric Loss Functions –

Download Bayesian Estimation of the Shape Parameter of Generalized Rayleigh Distribution Under Symmetric and Asymmetric Loss Functions. Mathematics students who are writing their projects can get this material to aid their research work.

Abstract

In 2001, Surles & Padgett introduced Generalized Rayleigh Distribution (GRD). This skewed distribution can be used quite effectively in modeling lifetime data.

In this work, Bayesian estimates of the shape parameter of a GRD were determined under the assumption of both informative (gamma) and non-informative (Extended Jeffery’s and Uniform) priors.

The Bayes estimates were obtained under both symmetric and asymmetric loss functions.

The performances of these estimates were compared to the Maximum Likelihood Estimates (MLEs) using Monte Carlo simulation.

Introduction

Statistical Inference is the branch of statistics concerned with using probability concept to deal with uncertainty in decision-making.

It refers to the process of selecting a sample and using a sample statistic to draw inference about a given population parameter.

The field of statistical inference is divided into the theory of estimation and hypothesis testing.

Statistical estimation or simply estimation is concerned with the methods by which population characteristics are estimated based on information drawn from a sample. The theory of estimation is further sub-divided into Point and Interval Estimation.

A point estimator is a random variable varying from sample to sample and its value is called point estimate i.e. a point estimate is a single value estimate for the parameter.

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