Estimation of the inverse function for random variate generation

Abstract

A regression method for estimating the inverse of a continuous cumulative probability function F ( x ) is presented. It is assumed that an ordered sample, X 1 , …, X n , of identically and independently distributed random variables is available. A reference distribution F 0 ( x ) with known inverse F 0 -1 ( p ) is used to calculate the quantities W i = i ln[ F 0 ( X i )/ F 0 ( X i +1 )]. These quantities are used to estimate the function γ ( p ) = pd ln≥ F 0 [ 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.