Characterizations and estimations of Size Biased Generalized Rayleigh Distribution

Abstract

Since the widely using of the weighted distribution in many fields of real life such various areas including medicine, ecology, reliability, and so on , then we try to shed light and record our contribution in this field thru the research. In this paper, a new class of size-biased Generalized Rayleigh distribution is defined. A size-biased Generalized Rayleigh distribution, a particular case of weighted Generalized Rayleigh distribution, taking the weights as the variate values has been defined. The power and logarithmic moments of this family is defined. Some important theorems of SBGRD has been derived and studied. A new moment estimation method of parameters of SBGRD using its characterization is presented. In brief, this paper consists of presentation of general review of important properties of the new distribution. Bayes estimators of Size biased Generalized Rayleigh distribution (SBGRD), that stems from an extension of Jeffery’s prior (Al-Kutubi [13]) with a new loss function (Al-Bayyati [12]). We are proposing four different types of estimator. Under squared error loss function, there are two estimators formed by using Jaffrey prior and an extension of Jaffrey’s prior. The two remaining estimators are derived using the same Jeffrey’s prior and extension of Jeffrey’s prior under a new loss function. These methods are compared by using mean square error through simulation study with varying sample sizes.

Keywords: Generalized Rayleigh distribution, Size biased generalized Rayleigh distribution, Logarithmic moment, squared error loss function, Al-Bayatti’s loss function.