TABLE OF CONTENTS This is the first of five chapters that comprise Part IV of the book. These chapters demonstrate RMM as a platform for empirical modeling of random variation. The claim of RMM for a "universal" character has been supported in earlier chapters by showing that a wide spectrum of existing scientific and engineering relational models, as well as current statistical models of random variation (namely, statistical distributions), are special cases of the RMM model (refer to Chapters 2 and 12). It is therefore appropriate that this part opens with a chapter that demonstrates the capability of the RMM error distribution to deliver satisfactory representation to variously shaped statistical distributions, which a practitioner may encounter in her/his daily routine.
In Chapter 10 fitting procedures for the RMM error distribution were developed. These procedures are used here to derive the RMM parameters that deliver best fit to some specified distributions. In Section 19.2 the RMM is fitted to some known distributions, assuming that the RMM errors are either normal or log-normal. The latter assumptions are shown to be essential to the effectiveness of the RMM model by assuming, in Section 19.3, that the errors are from another distribution, for example, the logistic distribution. The good accuracy obtained with normal or log-normal errors vanishes. What this might imply is discussed. In Section 19.4 new closed-form non-polynomial...
