Distribution Fitting with the Quantile Function of Response Modeling Methodology (RMM)

Authored by: Haim Shore

Handbook of Fitting Statistical Distributions with R

Print publication date:  October  2010
Online publication date:  April  2016

Print ISBN: 9781584887119
eBook ISBN: 9781584887126
Adobe ISBN:

10.1201/b10159-17

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Abstract

Distribution fitting aims to provide the data analyst with a general platform for modeling random variation. The need for such a “general-purpose” platform arises when either the available sample size is too small, or a priori knowledge about the source of the data is too scarce to identify with any acceptable degree of confidence the true underlying distribution. In such circumstances, distribution fitting proposes to substitute the unknown distribution by a member of a multi-parameter family of distributions, like the Johnson or Pearson families. It is assumed that such (known) families are flexible enough to deliver good representation to unknown distributions, no matter how diversely-shaped they might be in practice. Response Modeling Methodology (RMM), developed in the early nineties of the previous century (Shore, 2005, and references therein), provides such a platform. Although originally developed as a general methodology for empirical modeling of systematic variation (variation in a response traceable to variation of predictor variables correlated with the response), the quantile function of the RMM error distribution has been shown to deliver good representation to a wide range of variously shaped distributions. Furthermore, RMM reduces to some well-known distributions, approximations, and transformations for selected values of its parameters (Shore, (2004a), and (2005), Chapter 12).

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