Some further methods of discretizing the exponential distribution

Abstract

One method for discretizing the exponential distribution such that the discrefized values bear a resemblance to the continuous distribution is as follows. The density function will first be divided into N equiprobable intervals each of area 1/N. Some measure of central tendency of each interval will define the equiprobable values. In a previous study [1] the effects of using the mean and the median of the equiprobable intervals was noted. The measure of effectiveness used involved a comparison of the moments of the delay distribution for a simple queueing system based upon these measures of central tendency and known theoretical results. This paper will present the results of two extensions of the previously cited study [1]. It was shown that when using the mean of the equiprobable intervals one obtained “better” i.e., less biased, results for the moments of the delay distribution under question than when the medians of the intervals were used. Although these results were very good, on some subjective measure, a bias does exist for all higher moments of the delay distribution. One way to reduce this bias is to consider different measures of each equiprobable interval. This paper shows the results of using the rth root of the rth moment of each interval, corrected for the mean. A second concern arises when there is a limited amount of storage space in the digital computer for the discretized points.