Selecting the best statistical distribution with PROMETHEE and GAIA

Alessio Ishizaka, Philippe Nemery
Computers & Industrial Engineering, Volume 61, Issue 4, November 2011

Abstract

Three methods have previously been presented in the Computer and Industrial Engineering journal for the selection of a statistical distribution describing a data-set: the weighted sum model, the weighted multiplication model and data envelopment analysis. These methods are based on distinctive pre-set parameters, which results in three different rankings. In these approaches there is no interaction with the decision-maker (DM). This leads to the question: which method and result should a DM choose?

In this paper, we adopt another approach where the DM is the central actor. Based on the multi-criteria decision aid methods, PROMETHEE and GAIA, we show that different preference parameters (given by the DM) lead to different rankings. This is illustrated by the use of the Smart Picker Pro software. The use of such a software permits to perform an interactive sensitivity analysis in order to analyse changes in the ranking when the preference parameters are modified.

Finally, the extension, PROMETHEE GDSS, permits to obtain a group decision when several decision makers are involved in the decision problem. The GDSS Gaia Map of Smart Picker Pro (downloadable at www.smart-picker.com) highlights that DM2 and DM4 have similar rankings (DM2 and DM4 arrow point in the same direction in the picture below) whereas DM1 (DM1 arrow points in a different direction) has a different ranking compared to the other DMs. This graphical representation can facilitate a debate between the decision-makers.

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