An Approximate Algorithm of Generating Variates and Computing Probabilities for Nonuniform Continuous Statistical Distributions

Abstract

In many cases, real-world experimen tations are approximated by various stochastic probabilistic models when performing computer simulations. During simulation processes, random variate generations are required. However, a general and exact method to satisfy such a requirement is hard to find. An approximate method would most effectively remedy this situation. In this paper, we provide an approximate algorithm method which can be used to generate arbitrary continuous non uniform variates and to perform probability computing. The algorithm has a very good performance on convergence order, preserving monotonicity, and smoothness. In order to implement the algorithm, piecewise cubic polynomial and rational function are interpolated. Both preserve the monotonicity of the data from the distribution function or its inverse function. Spline methods are discussed. Simulation results are given.