TABLE OF CONTENTS Variation in the linear predictor (LP) provides the component of systematic variation in the response total variation. When the LP is constant, fluctuations in the response are random and their dispersion is described by the error distribution.
In this chapter the RMM error distribution is derived and its properties explored.
Setting the LP, ?, to a constant value, the RMM basic model (7.6) expresses the relationship between the response and the two (possibly correlated) errors, ? 1 and ? 2. From this relationship, various formulae can be obtained, like the density function (d.f) and the cumulative distribution function (CDF). These are then used to derive moments and other distributional properties, like the median and the mode.
In Section 9.2 basic expressions associated with the RMM error distribution are developed. In Section 9.3 we derive expressions for the moments and explore some other properties of the error distribution. Both sections relate to the basic model, given by (7.6) or (7.9). In Section 9.4 we introduce other variations of the basic RMM error distribution, corresponding to variations of the RMM basic relational model, developed in Chapter 7 [refer to (7.6abc), and to (7.12) and (7.13)]. The properties of these variations are left for the reader to explore.
In Chapters 10 and 11, fitting and estimation procedures, respectively, are developed. In Chapter 12 we show that the RMM error distribution, with its different versions, comprises as exact special cases some well-known families of distributions, response transformations and distributional...
