IOSR Journal of Engineering (IOSRJEN) www.iosrjen.org ISSN (e): 2250-3021, ISSN (p): 2278-8719 Vol. 10, Issue 12, December 2020, ||Series -II|| PP 19-26 International organization of Scientific Research 19 | Page Parameter Estimation of P-Dimensional Rayleigh Distribution under Different Loss Functions Arun Kumar Rao & Himanshu Pandey Department of Mathematics & Statistics DDU Gorakhpur University, Gorakhpur, INDIA Received 28 December 2020; Accepted 09 January2021 Abstract In this paper, p-dimensional Rayleigh distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and inverted gamma priors. Keywords Bayesian method, p-dimensional Rayleigh distribution, quasi and inverted gamma priors, squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions. I. INTRODUCTION The probability density function (pdf) of p-dimensional Rayleigh distribution is given by       2 2 1 2 0 0 2 p x p f x; e ; x , . p x            (1) (Cohen and Whitten [1]). The distribution with pdf (1), in which p=1, sometimes called the folded Gaussian, the folded normal, or the half normal distribution. With p=2, the pdf of (1) is reduced to two-dimensional Rayleigh distribution. With p=3, the pdf of (1) is reduced to Maxwell-Boltzmann distribution. Let 1 2 n x ,x , .......... ,x be a random sample of size n having probability density function (1), then the likelihood function of (1) is given by (Rao and Pandey [2])     2 1 1 2 1 1 2 2 n i i n n x np p i i f x; x e p                           (2) The log likelihood function is given by     1 2 1 1 1 2 2 2 n n p i i i i np log f x; nlog nlog p log log x x               (3) Differentiating (3) with respect to θ and equating to zero, we get the maximum likelihood estimator of θ which is given by 2 1 2 n i i x np      . (4) II. BAYESIAN METHOD OF ESTIMATION The Bayesian inference procedures have been developed generally under squared error loss function 2 L ,                    . (5) The Bayes estimator under the above loss function, say, s   is the posterior mean, i.e,