APPROXIMATIONS TO THE DISTRIBUTION FUNCTION OF SUMS OF INDEPENDENT CHI RANDOM VARIABLES.
STANFORD UNIV CALIF DEPT OF STATISTICS
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The problem is considered of approximating the distribution function, F sub n, where there are n independent standard normal random variables. Three well known approximations, the Edgeworth, the Cramer, and a Saddlepoint approximation are described. Another saddlepoint approximation is derived. The problem is discussed of calculating the moment generating function of F sub 1 for complex values of its argument. The four approximations to F sub n are compared for several cases and it is seen that the second saddlepoint approximation yields better results in each case. Author