Bootstrap Estimation for the β Distribution of Repeated Measurement Data

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.)