Five Popular Probability Density Functions: A Comparison in the Field of Stock-Control Models

Abstract

For the statistical description of a demand process, many probability density functions (pdf) are available, each having its advantages and drawbacks. How do they compare when in application? Is it true that the shape of the pdf is not relevant? This paper deals with one application, namely a simple s,Q stock control system. Assuming for the lead time demand successively five different pdf's (Gaussian, logistic, gamma, log-normal, Weibull) and using the service level as a criterion, it is shown that for this application (1) the numerical differences between the selected functions are in fact negligible; (2) the logistic pdf produces a formula that only contains elementary transcendental functions; (3) the other pdf's lead to much more complex expressions.