摘要
本文首先发现帕累托分布抽样基本定理,应用到帕累托分布参数估计中,得到了帕累托分布参数的一致最小方差无偏估计;并且得到了单总体帕累托分布参数的置信区间及联合置信区间,以及双总体帕累托分布参数比值的置信区间.
This article discovers the sampling theorem for the Pareto distribution,and applies it to the parametric estimation of Pareto distribution and related,such as uniformly minimum varmumiance unbiased estimator(UMVUE)of parameters of Pareto distribution,the confidence intervals and joint confidence region of parameters for one population,and confidence intervals of ratio of parameters for two populations.
引文
[1]李国安.指数分布抽样基本定理及在指数分布参数统计推断中的应用[J].大学数学,2016,32(5):30-36.
[2]Pareto V.Cours d’economie Politique,Vol.II[M].F.Rouge,Lausanne,1897.
[3]Pasari S,Dikshit O.Three-parameter generalized exponential distribution in earthquake recurrence interval estimation[J].Nat Hazards,2014,73:639-656.
[4]李国安.李建峰.指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用[J].数学的实践与认识,2017,47(3):165-169.
[5]Arnold B C.Univariate and multivariate Pareto models[J].Journal of Statistical Distributions and Applications,2014,1(11):1-16.
[6]Malik H J.Estimation of the parameters of the pareto distribution[J].Metrika,1970,15:126-132.
[7]Baxter M A.minimum variance unbiased estimation of parameters of the pareto distribution[J].Metrika,1980,27:133-138
[8]Kern D M.minimum variance unbiased estimation in the pareto distribution[J].Metrika,1983,30:15-19.
[9]Saksena S K,Johnson A M.Best unbiased estimator for the parameters of a two-parameter pareto distribution[J].Metrika,1984,31:77-83.
[10]Zhenmin Chen.Joint confidence region for the parameters of pareto distribution[J].Metrika,1996,44:191-197.
[11]Hui He,Na Zhou,Ruiming Zhang.On estimation for the Pareto distribution[J].Statistical Methodology,2014,21:49-58.