Comparative Descriptive Statistics of Skewed Probability Distributions
Abstract
This report addresses a technical issue in the current practice of operational analysis (OA). Increasingly, OA studies involve simulations of varying levels of sophistication. A feature of all simulations is the use of random variables, and this immediately raises the question of what distribution to employ. Should the random variable be taken as uniformly distributed over some range, should it follow a bell curve with some mean and standard deviation, or should it be exponentially distributed? Sometimes there are methodological or theoretical arguments favoring a particular distribution. In their absence, the modeler is forced to make an arbitrary choice of distribution, motivated perhaps by ease of use or personal familiarity. It then becomes interesting to know how sensitive the results of the analysis are to the choice of distribution: if another had been chosen, would the conclusions have been different? This report is a brief handbook on the comparative descriptive statistics of a wide variety of skewed probability distributions, both continuous and discrete. The aim is to facilitate the comparison of different distributions for use where random variables are employed without any firm information on their probability distributions. In this situation it is of interest to look for sensitivity to the distribution chosen. This can best be done by running the model with a variety of distributions, which then raises the question of how to compare distributions. The report advocates the use of moments and presents the requisite equations. As obvious as this approach may appear, many of the equations do not seem to have been published previously and some of the results are apparently wholly new. A total of 18 distributions are treated in detail, including all of the most commonly used skewed probability distributions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 2004
- Accession Number
- ADA426898
Entities
People
- M. P. Fewell
Organizations
- Defence Science and Technology Group