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

© 2022 Global Journals 1 Year 2022 38 Global Journal of Science Frontier Research Volume XXII Issue ersion I V IV ( F ) On Baysian Estimation of Loss of Estimators of Unknown Parameter of Binomial Distribution Let the random variable X follows binomial distribution with parameters n and θ .Where θ is unknown satisfying 0 ≤ θ ≤ 1.The prior p.d.f of θ ,denoted by π 1 ( θ ) is as follows: π 1 ( θ ) = ( θ α − 1 (1 − θ ) β − 1 B ( α,β ) if α ≥ 0, β ≥ 0,0 < θ < 1 0 O therwise (2.1) Under the assumption of prior probability density function (p.d.f.) for θ as above,Bayes estimates of θ derived by Rukhin (1988) were as follows: For α ≥ 0 , β ≥ 0 δ B ( X ) = ( X + α ) ( n + α + β ) (2.2) γ B ( X ) = ( X + α )( n + β − X ) ( n + α + β ) 2 ( n + α + β + 1) (2.3) and for α = 0 , β = 0 δ 0 ( X ) = X n (2.4) γ 0 ( X ) = X ( n − X ) n 2 ( n + 1) (2.5) It was shown that E θ L ( θ, δ 0 , γ 0 ) = ∞ (2.6) Under, w 1 ( θ, δ ) as above, the corresponding Bayes estimate is given by, For α ≥ 0 , β ≥ 0 δ 1 B ( X ) = E { θh ( θ ) /X } E { h ( θ ) /X } (2.7) Or, δ 1 B ( X ) = ( X + α − 1) A − 2 (2.8) On simplification,provided, A = n + α + β > 2 and, γ 1 B ( X ) = E { θh ( θ ) /X } − { δ 1 B ( X ) } 2 E { h ( θ ) /X } (2.9) N otes E stimation of L oss and R isk of the P arameter of B inomial D istribution II.