A flexible method for estimating inverse distribution functions in simulation experiments

To generate random variates from an unknown continuous distribution, we present procedure IDPF – a flexible technique for estimating the associated inverse distribution function from sample data and for generating variates from the fitted distribution by inversion. To motivate IDPF, first we examine a predecessor due to Hora, and we explain how Hora's method can fail in either the distribution-fitting or variate-generation stage of application. We apply IDPF as follows. After selecting an initial inverse distribution function by a standard technique, we estimate a polynomial ‘filter’ for the random-number input by constrained nonlinear regression to achieve minimum ‘distance’ between the empirical inverse distribution and the final fitted inverse distribution obtained by composition of the initial inverse distribution with the polynomial ‘filter’. The regression constraint ensures that the fitted inverse distribution function is nondefective and monotonically nondecreasing. A portable, public-domain implementation of IDPF is based on well-known techniques for selecting initial distributions from the Johnson translation system. A Monte Carlo study illustrates the effectiveness of IDPF. Compared to initial Johnson distributions selected by matching moments, IDPF-based fits are closer on the average to the corresponding empirical and theoretical inverse distribution functions. Similar conclusions apply to other initial distributions selected by other methods.