An approximate method for generating asymmetric random variables
Communications of the ACM
An approximate method for generating symmetric random variables
Communications of the ACM
Optimization Techniques with FORTRAN
Optimization Techniques with FORTRAN
WSC '77 Proceedings of the 9th conference on Winter simulation - Volume 1
Weighted quantile-based estimation for a class of transformation distributions
Computational Statistics & Data Analysis
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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.