The asymptotic inversion of certain cumulative distribution functions
N. M. Temme (Centre for Mathematics and Computer Science, The Netherlands)
The inversion of cumulative distribution functions is an important topic in statistics, probability theory and econometrics, in particular for computing percentage points of chi-square, F, Student's t-distributions, and the Erlang B formula. For large parameters the numerical inversion of these distributions Newton's method needs accurate starting values, and for the standard distributions powerful asymptotic formulas can be used to obtain these values..
In this talk we demonstrate how uniform asymptotic expansions of the incomplete gamma functions and incomplete beta function, which are the basic functions for several distribution functions, can be used for the asymptotic inversion of these functions. Other examples will also be discussed.