BAYESAIN ESTIMATION OF SIZE BIASED CLASSICAL GAMMA DISTRIBUTION
Keywords:
Size Biased Gamma Distribution, Jeffrey’s Prior and Extension of Jeffrey’s Prior, Loss Functions, Software.Abstract
Journal of Reliability and Statistical Studies; ISSN (Print): 0974-8024, (Online):2229-5666 Vol. 0, Issue 1 (2014): 31- 42 BAYESAIN ESTIMATION OF SIZE BIASED CLASSICAL GAMMA DISTRIBUTION J. A. Reshi1, A. Ahmed2 and K. A. Mir3 1,2Department of Statistics, University of Kashmir, Srinagar, India. 3Department of Statistics, Govt. Degree College Bemina Srinagar, India. E Mail: 1reshijavaid19@gmail.com Received July 31, 2013 Modified April 07, 2014 Accepted May 21, 2014 Abstract In this paper, we present Bayes’ estimator of the parameter of Size biased Gamma distribution (SBGMD), that stems from an extension of Jeffery’s prior (Al-Kutubi (2005)) with a new loss function (Al-Bayyati (2002)). We are proposing four different types of estimators. 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. We are also deriving the survival function of the size biased Gamma distribution. These methods are compared by using mean square error through simulation study with varying sample sizes.
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