臺灣博碩士論文加值系統

已經有許多作者討論過相互獨立卡方隨機變數之加權和的近似分配，這些結果可以被用來結合許多獨立的顯著檢定。不過有一些情況，這些個別的檢定是有相關的。因此，結合後的檢定統計量就不再是獨立的卡方隨機變數的加權和。本篇文章將研究有相關或不相關的卡方隨機變數做加權和之後的近似分配。在此我們提出兩種近似分配，其一是卡方近似分配，另一個是常態近似分配，並且計算兩種近似法的誤差，及利用模擬比較兩者的優劣。

Many authors have discussed the approximate distribution of a weighted sum
of mutually independent chi-squared random variables. The results of previous
studies can be used to combining independent tests of significance. In some situations,
the individual tests are correlated. Thus the test statistic is no longer
a weighted sum of independent chi-squared variables. This paper studies the
approximate distribution of a weighted sum of correlated or uncorrelated chisquared
variables. This approximate distribution can be obtained by two types
of approximations, namely the chi-squared approximation and the normal approximation.
This study calculates the error bounds of both approximations, and
compares using simulations.

1. Introduction
2. Main Results
3. Simulation
4. Conclusion

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