Distribution of a Sum of Weighted Noncentral Chi-Square Variables
Distribution of a Sum of Weighted Noncentral Chi-Square Variables
复制标题
DOI：
10.5351/ckss.2006.13.2.429
复制
发表时间：
2006-08
影响因子：
0.4
通讯作者：
Sun-Yeong Heo;Duk-Joon Chang
中科院分区：
文献类型：
--
作者：
Sun-Yeong Heo;Duk-Joon Chang
在统计计算中，研究人员经常需要非中心卡方变量的加权和的分布。在这种情况下，要知道它的确切分布是非常有限的。有许多著作对这一主题做出了贡献，例如Imhof（1961）和Solomon-Stephens（1977）。Imhof的方法给出了很好的近似的真实分布，但它是不容易应用，即使我们考虑到计算机技术的发展Solomon-Stephens的三阶矩卡方近似是相对容易和准确的应用。然而，他们跳过了许多细节，并且他们的模拟仅限于中心卡方随机变量的加权和。本文详细介绍了Solomon-Stephens方法。我们还将他们的模拟推广到非中心卡方分布的加权和。我们评估了齐次检验的近似功效，并将其与真实功效进行了比较。Solomon-Stephens方法对这种情况显示出很好的近似性。
In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.