APPROXIMATIONS TO THE DISTRIBUTION FUNCTION OF SUMS OF INDEPENDENT CHI RANDOM VARIABLES.
TL;DRAbstract
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)
Chat with Paper
AI Agents for this Paper
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)
Keywords
Chat
Click to start Chat