Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

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.