Monte Carlo Simulation Using Moments of Random Variables

Abstract

In the present study, in order to include the random variables with an unknown cumulative distribution function (CDF) into Monte-Carlo Simulation, an inverse normal transformation is suggested. The random variables with an unknown CDF are expressed as a simple function of a standard normal random variable, and the function is determined using the first few statistical moments which are generally available from the statistical data of the random variables. Using the proposed method, the random numbers of random variables with an unknown CDF can be easily generated utilizing those of a standard normal random variable, which is generally considered to be quite easily generated. Some examples are presented from which the efficiency of the method is investigated. It is found that although the method is quite simple, it is accurate enough to include the random variables with unknown CDF in the Monte-Carlo Simulation for structural reliability.