相依正隨機變數之合其分佈函數之最佳化超立方體估計

Abstract

在給定聯合分佈函數之下，對於計算多個相依的正隨機變數合之分佈函數以及機率函數，我們提供一個最佳化的幾何數值方法。這個方法包含對超立方體的積分並估計”半”超立方體的體積。同時我們也提供了數值分析的結果。

We present optimal geometric numerical methods for computing the distribution function and the density function of sum of several positive dependent random variables with known joint distribution function. This method involves integration on high dimensional hypercubes and estimating the volume of "half" hypercubes. Numerical results are also presented.