Estimation of the inverse function for random variate generation
A regression method for estimating the inverse of a continuous cumulative probability function F(x) is presented. It is assumed that an ordered sample, X1, …, Xn, of identically and independently distributed random variables is available. A reference distribution F0(x) with known inverse F0-1(p) is used to calculate the quantities Wi = i ln[F0(Xi)/F0(Xi+1)]. These quantities are used to estimate the function &ggr;(p) = pd ln≥F0[F-1(p)]⋦/dp from which an estimate of F-1(p) is derived. The method produces an estimate in a form that is convenient for random variate generation. The procedure is illustrated using data from a study of oil and gas lease bidding.