Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

Azam Zaka,Ahmad Saeed Akhter

doi:10.18187/pjsor.v10i2.657

Abstract

Nakagami distribution is a flexible lifetime distribution that may offer a good fit to some failure data sets. It has applications in attenuation of wireless signals traversing multiple paths, deriving unit hydrographs in hydrology, medical imaging studies etc. In this research, we obtain Bayesian estimators of the scale parameter of Nakagami distribution. For the posterior distribution of this parameter, we consider Uniform prior, Inverse Exponential prior and Levy prior. The three loss functions taken up are Squared Error Loss Function (SELF), Quadratic Loss Function (QLF) and Precautionary Loss Function (PLF). The performance of an estimator is assessed on the basis of its relative posterior risk. Monte Carlo Simulations are used to compare the performance of the estimators. It is discovered that the PLF produces the least posterior risk when uniform priors is used. SELF is the best when inverse exponential and Levy Priors are used.

Highlights

Nakagami distribution was proposed for modeling the fading of radio signals (Nakagami, 1960)
Nakagami distribution is a flexible lifetime distribution model that may offer a good fit to some sets of failure data
The posterior risk based on all priors and for all loss functions, relating to the scale parameter of a Nakagami distribution, expectedly decrease with the increase in sample size

Summary

Introduction

Nakagami distribution was proposed for modeling the fading of radio signals (Nakagami, 1960). The nakgami-m distribution is widely used to model the fading of radio signals and other areas of communicational engineering (Statistical Distributions by Peacock) It can be used in hydrology to derive the unit hydrographs. Kazmi et al (2012) compared class of life time distributions for Bayesian analysis They studied properties of Bayes estimators of the parameter using different loss functions via simulated and real life data. The Bayes estimators for the scale parameter is derived in Inverse Weibull distribution, by considering Quasi, Gamma and uniform priors under square error, entropy and precautionary loss function. 2. Posterior Distributions under the Assumption of Different Priors The objective of this chapter is to find Bayesian estimators of the scale parameter of Nakagami distribution under various loss functions and priors. The Posterior distribution of scale parameter using Levy Prior is d 2 n )

Bayesian Estimation Under Three Loss Functions

Simulation Study

Summary and Conclusions