Abstract: The estimation of the functionθ=exp{αμ+bσ²} of parameters (μ,σ²) in normal distribution N(μ,σ²) is discussed. And when the prior distributions of μ and σ² are independent, under the loss function L(θ,δ)=(θ^-1×δ-1)², the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.

Key words:  normal , distribution;logarithmic , normal , distribution;prior , distribution, Bayesian estimation;minimax estimation