Friday, October 22, 2010

Stochastic Ordering: from the Lorenz curve to Quality Control

Manuel Cabral Morais

Abstract: Lorenz (1905) is a landmark in the history of Stochastic Ordering (SO). Feeling that all of the summary measures under consideration in the comparison of income inequality constituted too much condensation of the data, Lorenz proposed a curve and suggested the following interpretation rule: the population with a higher level of income inequality is associated to a more bent (Lorenz) curve. Since then SO (Shaked and Shanthikumar, 2007) has gained widespread acceptance and is a well-established research topic with applications in Actuarial Science, Biology, Economics, Queueing, Operations Research, Reliability, Risk Theory, Scheduling, Statistical Inference (Shaked and Shanthikumar, 1994) and several other areas. This paper will focus on a brief overview of SO and on two applications. In Finance, SO is particularly important in portfolio selection (Müller and Stoyan, 2002). The application of SO to First Passage Times arising in Quality Control provides decisive insights into how quality control schemes work in practice and allows the performance comparison of competitive control schemes (Morais, 2002). References: Lorenz, M.O. (1905). Methods of measuring the concentration of wealth. Publication of the American Statistical Association 9, 209-219. Shaked, M. and Shanthikumar, J.G. (1994). Stochastic Orders and Their Applications. Academic Press, London. Shaked, M. and Shanthikumar, J.G. (2007). Stochastic Orders. Springer-Verlag, New York. Morais, M.J.C. (2002). Stochastic Ordering in the Performance Analysis of Quality Control Schemes. Ph.D. Thesis, DM-IST, UTL. Supervisor: Prof. Dr. A. Pacheco Pires. Müller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. John Wiley & Sons, Chichester.

Friday, October 22, 2010
Time: 11h00
Room: Sala IAPMEI, Edificio Quelhas, ISEG