广义正态分布族及其应用

A Class of Generalized Normal Distribution and Application

摘要: 本文研究了一类新的分布函数族，称之为广义正态分布族。广义正态分布族不仅包含了原有的正态分布，还拓展出了一族新的分布，且能刻画具有非对称、多峰、厚尾等特征的数据，具有很好的灵活性。本文首先研究了广义正态分布族的分布函数以及密度函数图像，通过观察图像形状的变化，并研究广义正态分布族的性质。然后将这一新分布应用到房价指数数据分析中，通过分析说明了广义正态分布族的有用性。

Abstract: In this paper, we study a new class of distribution, called as generalized normal distribution. It can not only include the standard normal distribution, but also expand a new class of distribution which can describe the data with the features such as asymmetry, multimodal, heavy-tail and has good flexibility. We firstly investigate the generalized normal distribution by the images of distribution and density functions, and study its properties. Then we apply the new class of distribution to the new housing price index data, and the usefulness of generalized normal distribution can be examined by the real data analysis.