Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 22 Issue 4

On Baysian Estimation of Loss of Estimators of Unknown Parameter of Binomial Distribution Randhir Singh Author: Department of Statistics, Ewing Christian College, Prayagraj, India. e-mail: dr.singh.ecc@gmail.com I. I ntroduction 1 Year 2022 37 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) Rukhin(1988) introduced a loss function given by, L ( θ, δ, γ ) = w ( θ, δ ) γ − 1 2 + γ 1 2 (1.1) Where, γ is an estimator of the loss function w ( θ, δ ) ,which is non-negative. Guobing(2016) used this loss function and derived estimates of the loss and risk function of the parameter of Maxwell’s distribution.Singh (2021) took various forms of w ( θ, δ ) and derived estimates of the loss and risk function of the parameter of a continuous distribution which gives Half-normal distribution,Rayleigh distribution and Maxwell’s distribution as particular cases. Rukhin(1988) considered the Bayesian estimation of the unknown parameter θ of the binomial distribution by taking w ( θ, δ ) = ( θ − δ ) 2 (1.2) In this paper,Bayes estimate of the unknown parameter θ of the binomial distribution has been obtained by replacing w ( θ, δ ) by w 1 ( θ, δ ) given by w 1 ( θ, δ ) = h ( θ )( θ − δ ) 2 (1.3) Where, h ( θ ) = 1 { θ (1 − θ ) } (1.4) N otes Summary- This paper aims at the Bayesian estimation for the loss and risk functions of the unknown parameter of the binomial distribution under the loss function which is different from that given by Rukhin(1988). The estimation involves beta distribution, a natural conjugate prior density function for the unknown parameter. Estimators obtained are conservatively biased and have finite frequentist risk. Keywords: Bayes Estimator, Loss Function, Risk Function, Binomial Distribution.