To summarize, many real-world problems fall naturally within the framework of normal theory. It turns out, however, that normal distributions are useful in practice for two reasons: First, the normal distribution serves as a bonafide population model in some instances second, the sampling distributions of many multivariate statistics are approximately normal, regardless of the form of the parent population, because of a central limit effect. Of course, mathematical attractiveness per se is of little use to the practitioner. This is frequently not the case for other data-generating distributions. One advantage of the multivariate normal distribution stems from the fact that it is mathematically tractable and "nice" results can be obtained. While real data are never exactly multivariate normal, the normal density is often a useful approximation to the "true" population distribution. In fact, most of the techniques encountered in this book are based on the assumption that the data were generated from a multivariate normal distribution. A generalization of the familiar bell-shaped normal density to several dimensions plays a fundamental role in multivariate analysis.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |