fitting a distribution to data using an alternative to moments
A four-parameter probability distribution that is useful in fitting data is considered. This distribution can approximate many well-known distributions and provides a simple and effective algorithm for generating random variates. Its utility, however, is limited by one's ability to determine its parameters. The method of moments has been suggested as a means of selecting the four parameter values when the first four moments are specified or can be estimated. Sample moments, however, are sensitive to extreme observations and are subject to large sampling variability. Hence, the method of moments is generalized to allow the use of surrogate measures of location, scale, symmetry, and tailweight. A new procedure using two statistics that are functions of order statistics is developed and is compared with the method of moments by means of an example and a Monte Carlo study.
moments order statistics monte carlo systems of probability distributions data fitting