重复测量数据β分布的自助法估计  

Bootstrap Estimation for the β Distribution of Repeated Measurement Data

作　　者：林洪桦[1] 潘峰[2] 

机构地区：[1]北京理工大学机械与车辆工程学院,北京100081 [2]北京理工大学信息科学技术学院自动控制系,北京100081

出　　处：《北京理工大学学报》2004年第11期947-951,共5页Transactions of Beijing Institute of Technology

摘　　要：统一采用有界的β(g,h)分布表示重复测量数据的各种概率分布。并提出按小样本估计β分布参数的"界似"与"形似"两种方法,先分别应用Bootstrap方法即自助法估计其均值和标准差、偏度和峰度,再按其间的关系求得其参数估计(g^,h^)。因(g^,h^)覆盖范围较大,在求解非线性方程组中同时采用Levenberg-Marquardt算法和遗传算法进行互校。通过Matlab软件(含仿真验证)易于在微机上实现。Uniform expression of the probability distribution of repeated measurement data by bounded β(g, h) distribution is recommended. Two kinds of estimation methods for the β distribution parameters according to small sized samples are presented. They are respectively the method of approximation boundary and the method of approximation shape. Using the bootstrap method to estimate the mean and standard deviation or skewness and kurtosis respectively, and then based on their relation the parameter estimations-(g^, h^) are obtained. The Levenberg-Marquardt method and genetic method are introduced to solve the nonlinear functions and check the results for each other, considering the large overlay range of (g^, h^). Calculation program (including simulate verification) using Matlab are made so that it can be easily realized on (the computer.)

关 键 词：误差分布 统示法 β分布 BOOTSTRAP方法 遗传算法 

分 类 号：P207.1[天文地球—测绘科学与技术]