A Normal-Based Monotone Convex Transformation, with Continuous Convexity, as an Alternative to the Concept of 'Distribution'?

• Activity Number: 307
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Haim Shore*+
• Companies: Ben-Gurion University of the Negev
• Keywords: Convex transformation? ; Distribution fitting ; L2 norm? ; Modeling ; Response Modeling Methodology (RMM)?

Abstract

Recently, a new modeling methodology, Response Modeling Methodology (RMM), had ?been suggested to model both systematic variation and random variation. The core of ?this approach is a new monotone convex transformation, based on normal quantiles, that ?models convexity as a continuous spectrum. This allows for the final form of the ?estimated transformation to be determined by the data rather than in advance. ?Cumulative experience has shown that RMM models are capable of representing not ?only widely used models in science and engineering but also diversely-shaped ?distributions. Monte-Carlo simulation results have shown that it is practically ?impossible to distinguish (in terms of L2-norm values) between an estimated RMM ?density function and that associated with the data-generating distribution. In this ?presentation we introduce the RMM approach and its principles. ?