Parameter Estimation of Power Rayleigh Distribution Using Real Data Sets Sofi Mudasir 1 , A. A. Bhat 2 , S. P Ahmad 3 , Aasimeh Rehman 4 1,2,3 Department of Statistics, University of Kashmir, Srinagar, India 4 Department of Psychology, University of Kashmir, Srinagar, India Abstract In this paper, we present the classical and Bayes estimators of power Rayleigh distribution under the combination of different priors and loss functions. The performance of the priors and loss functions has been compared in terms of the posterior variance and posterior risk using real life data sets. Keywords: Power Rayleigh distribution, maximum likelihood estimation, Bayesian estimation and real data. 1. Introduction Rayleigh distribution is a continuous lifetime distribution introduced by John William Rayleigh (1880) in connection with a problem in the field of acoustics and has wide range of applications including life testing experiments and clinical studies. One of the major applications of the Rayleigh distribution is to analyzing the wind speed data. This distribution is a special case of Weibull distribution with the shape parameter equal to 2. The origin and other aspects of this distribution can be found in Siddique (1962). There are number of authors who contributed to this model, among them are Al-Buhairi (2006), Abd Elfattah et al. (2006), Ghazal and Hasaballah (2017), Sofi et al. (2019) and Bhat and Ahmad (2020). The probability distribution function (pdf) and cumulative distribution function (cdf) of power Rayleigh distribution with scale parameter  and shape parameter  is given by   . 0 , , 0 , 2 exp , | 2 2 1 2 2                       v v v v f (1)   . 2 exp 1 , | 2 2                v v F (2) The objective of this article is to estimate the parameters of the said model through classical and Bayesian methods of estimation and to make comparison among different priors and loss functions using real life data sets. The article is organized as follows: section 2 proposes the classical and Bayes estimators of the parameters under the combination of different priors and loss functions. Section 3 introduces the posterior mean and posterior variance under different priors. Section 4 is devoted to illustrative examples using real life data sets and section 5 is the discussion. GIS SCIENCE JOURNAL VOLUME 7, ISSUE 12, 2020 ISSN NO : 1869-9391 PAGE NO: 290