【摘要】 讨论正态分布N(μ,σ2)的参数(μ,σ2)的函数θ=exp{aμ+bσ2}(a≥0,b≥0)的估计问题,给出了θ的最大似然估计及矩估计.在μ和σ2的先验分布独立时,在损失函数L(θ,a)=(θ-a)2和L(θ,a)=(θ-1×a-1)2下给出Bayes估计和最小最大估计.更多还原

【Abstract】 The estimation of the function θ=exp{aμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed.Maximum likelihood estimation and square estimation are given,and when the prior distributions of μ and σ2 are independent the Bayesian estimation of the function θ=exp{aμ+bσ2} of parameters (μ,σ2) is obtained under the loss function L(θ,a)=(θ-a)2 and L(θ,a)=(θ -1×a-1)2.更多还原