A General Approximation to the Distribution of Count Data with Applications to Inventory Modeling

38 Pages Posted: 12 Apr 2007 Last revised: 5 Jul 2008

See all articles by Edward Fox

Edward Fox

Southern Methodist University (SMU) - Marketing Department

Bezalel Gavish

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM)

John H. Semple

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM)

Date Written: March 31, 2008

Abstract

We derive a general approximation to the distribution of count data based on the first two moments of the underlying interarrival distribution. The result is a variant of the Birnbaum-Saunders (BISA) distribution. This distribution behaves like the lognormal in several respects; however, we show that the BISA can fit both simulated and empirical data better than the lognormal and that the BISA possesses additive properties that the lognormal does not. This results in computational advantages for operational models that involve summing random variables. Moreover, although the BISA can be fit to count data (as we demonstrate empirically), it can also be fit directly to transaction-level interarrival data. This provides a simple, practical way to sidestep distributional fitting problems that arise from count data that is censored by inventory stockouts. In numerical experiments involving dynamic inventory models, we compare the BISA distribution to other commonly used distributions and show how it leads to better managerial decisions.

Keywords: Birnbaum-Saunders, inverse Gaussian, gamma, confluent hypergeometric functions, news vendor model

Suggested Citation

Fox, Edward and Gavish, Bezalel and Semple, John H., A General Approximation to the Distribution of Count Data with Applications to Inventory Modeling (March 31, 2008). SMU Cox School of Business Research Paper No. 07-002. Available at SSRN: https://ssrn.com/abstract=979826 or http://dx.doi.org/10.2139/ssrn.979826

Edward Fox (Contact Author)

Southern Methodist University (SMU) - Marketing Department ( email )

United States

Bezalel Gavish

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM) ( email )

Dallas, TX 75275
United States

John H. Semple

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM) ( email )

Dallas, TX 75275
United States
214-768-2546 (Phone)
214-768-4099 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
131
Abstract Views
966
rank
219,757
PlumX Metrics