Tables for the Studentized Largest chi-Square Distribution and Their Applications

摘要

Let x sub 1,...,x sub K be K independently distributed chi-square variates with n degrees of freedom and let x sub 0 be another chi-square variate with m degrees of freedom distributed independently of the other x sub i's. Then, the distribution of u = mxmax/nx sub 0 where xmax = max (x sub 1,...,x sub K), is known to be the studentized largest chi-square distribution. In this report, two methods are proposed to evaluate the probability integral of u. Using one of these methods, upper 10%, 5%, 2.5% and 1% points of the distribution of u are tabulated for K = 1(1)12, n = 1(1)19 and for different values of m. Various applications of these tables are also discussed. (Author)