The generation of piecewise linear approximations of probability distribution functions

Abstract

An iterative non-linear technique is described for approximating a given probability distribution function or set of experimental observations by fitting a subset of their moments to a piecewise linear distribution function. This approximate function may then be used for generating simulated observations from the given function or experimental data. The technique has the advantage over conventional approximation procedures in that it minimizes the number of coordinate pairs required as descriptors, it reproduces the lower order moments of the given function or data, and it may be used for any set of data, regardless of the form of the underlying distribution. The procedure is demonstrated with several sets of experimental data, and with the standard normal and Erlang-k distribution functions.