Response modeling methodology (RMM) - Current distributions, transformations, and approximations as special cases of the RMM error distribution

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Recently a new Response Modeling Methodology (RMM) has been introduced, which models the relationship between a response and the affecting factors, assuming only that this relationship is monotone convex. It has been demonstrated that many current relational models, developed over the years in various branches of engineering and the sciences, are in fact special cases of the RMM model. In this paper, we proceed to demonstrate that the RMM error distribution delivers as special cases some well-known statistical distributions, or related transformations and approximations. This establishes the RMM error distribution as a highly versatile platform for modeling random variation. New accurate non-polynomial approximations to the CDF of the normal distribution, with absolute error less than 0.00002, and to the Poisson quantile function, demonstrate this versatility.

Original languageEnglish
Pages (from-to)1491-1510
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Volume33
Issue number7
StatePublished - 1 Jul 2004

Keywords

  • Approximations to the normal and Poisson distributions
  • Box-Cox transformation
  • Empirical modeling
  • Error distribution
  • Johnson transformations
  • Response modeling methodology
  • Tukey's distributions

Fingerprint

Dive into the research topics of 'Response modeling methodology (RMM) - Current distributions, transformations, and approximations as special cases of the RMM error distribution'. Together they form a unique fingerprint.

Cite this