有限個數的i.i.d. Weibull分布隨機變數之和的機率分布函數的近似值

Abstract

我們的目的 , 是要找 有限的i.i.d. Weibull 分佈隨機變數之和 的機率分佈函數 的近似值 . 如果用Edgeworth 近似法 , 則由於它的不對稱性使得效果不好 . 因此 , 我們要找一個簡單 , 優美且準確的近似法 . 我們已找到一個 , 且由數值計算得知效果很好 . 剩下來的部分是理論的證明 .

Our goal of this project is to find an approximation of the distribution function of the sum of finite number of i.i.d. Weibull random variables. Implicitly, high asymmetry in the shape of the density function of the Weibull random variable with the shape parameter c < 1 may cause low efficiency in estimating the density function if we use Edgeworth approximation. Thus, the major goal of this project is to find a simple, elegant and relatively accurate form of an approximation. Some numerical result we have studied shows that our approximation achieved these requirements. The theoretical part is the major work in this project.