广义数学期望

Generalized Mathematical Expection

本文应用 H.L.P.均值于样本,构造了广义样本均值;为了将它用于参数估计,根据替换法则(Substitution rule),推广了数学期望的定义,同时引入新的无偏性.最后应用广义数学期望的基本性质推出若干结论(定理1～4),说明在参数估计方面应用广义均值是有意义的.

This paper constructs the generalized sample means using Hardy-Litt- lewood-Polya mean,defines the generalized mathematical expectation in parallel,gives a definition of generalized unbiasedness and results in rene- wal of substitution rule.It has been proved that the geometrical mean E_gX is a geometrical unbiased estimation of the parameter λ=e~μ while arithmetic mean EX is not a unbiased one if r.v.X obeys logarithmic normal distribu- tion.Besides this,the similar results of parameter estimation of weibull or gam- ma distribution have been obtained.All of these show that generalized mathe- matical expectation is a useful tool in probability theory and statistics.