A method for multi-parameter PDF estimation of random variables

he probability distribution function (PDF) of a random variable Z is approximated with c.e(Q(z)), where Q(z) is a polynomial function and c is normalizing constant. Based upon the weighted residual method, general linear algebraic equations have been derived for the evaluation of the unknown parameters in the polynomial. Numerical examples are presented and the results show that the PDFs obtained using the proposed method converge to those obtained from Monte Carlo simulation as the number of parameters in the approximate PDF increases. (C) 1998 Elsevier Science Ltd. All rights reserved.