Inverse Cumulative Approximation and Applications
M. E. Tarter · Biometrika · 1968
The following general problem is considered: fit the inverse cumulative distribution function F−1(y) by a polynomial expansion in terms of a more tractable function G−1(y).It is shown that the computation of the coefficients of this expansion need not depend upon the evaluation of F−1(y) for specific values of y, but instead can be based on the evaluation of the cumulative F(x). If G−1(y) is chosen to be - log (1 - y), the solution in this particular case is shown to be based upon the Laguerre polynomials. Applications of the above methods are briefly described for such problems, as: random number generation, order statistic moment and product moment calculation, as well as the smoothing of the sample cumulative.