广义Lambda分布及其在数据选配上的应用

The Generalized Lambda Distribution and its Uses in Fitting Data

本文首先介绍含有四个参数的广义Lambda分布。该分布包括多种多样的曲线类型;由于它具有灵活、普遍与简易的特点,故适用于解决基础模型尚未发现情况下的数据表达问题。其次介绍广义Lambda分布的两种参数估计方法——矩估计法和非线性最小平方估计法,并用Monte Carlo模拟试验对这两种方法进行比较。最后,用两个数字实例对矩估计法和非线性最小平方估计法加以具体的说明。

In this article a generalized Lambda distribution with four parameters is presented firstly.It includes a wide variety of curve shapes, and because of the flexibilty, generality and simplicity of the distribution, it is useful in the representation of data when the underlying model is unknown.Secondly, two methods for estimating the parameters of the generalized Lambda distribution are proposed:method of moments estimation and nonlinear least squares estimation method. Then they are compared with each other by using Monte Carlo Simulation Test. Finally, two numerical examples are given to illustrate the methods of moments estimation and the nonlinear least squares estimation.