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 language | English |
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Pages (from-to) | 1491-1510 |
Number of pages | 20 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 33 |
Issue number | 7 |
State | Published - 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
ASJC Scopus subject areas
- Statistics and Probability