Identifying a Two-Parameter Distribution by the First two Sample Moment (Partial and Complete)

Abstract

Current exploratory procedures to identify distributions in simulation modeling often use statistics which have relatively low power in distributional “goodness-of-fit” tests. When sample data are scarce, this may lead to a misidentification of the true distribution and ultimately to a misrepresentation of the investigated system.

In this paper, a new exploratory procedure for identifying a two-parameter distribution is proposed. The procedure calculates, for each candidate distribution, two distribution-specific estimates of skewness, and then selects as the most likely distribution the one with the smallest absolute deviation between the two estimates. Both skewness estimates are associated with mean squared errors considerably smaller than that of the sample skewness.

A comprehensive simulation study compares the effectiveness of the new procedure to that of traditional methods for distributional identification. Distributional mis-specification rates of the new procedure are found to be similar to those of current methods, however the new approach possesses certain desirable properties which are discussed.

Keywords:

• Approximations
• Distribution fitting
• Exploratory analysis
• Simulation