ABSTRACT
A common procedure for looking at the level of organization of any data set is to study the probability density function (PDF) or the cumulative density function (CDF). In particular, cumulative hypergeometric frequency distributions have been found in many areas of the natural sciences (see, for example, Laherrere and Sornette 1998 for a review) and imply a wide range of values with many small values and few large values. This chapter focuses on several aspects of the cumulative frequency distribution of self-similar and self-afne patterns. This includes theoretical investigations of the correspondence between cumulative distribution functions and probability density functions (Section 5.1) and the descriptions of the frequency distributions of intensities, areas, and volumes (Sections 5.2, 5.3, and 5.4). Special attention is nally given to rank-frequency distributions, from their original development in linguistics and their link to information theory and entropy to their effectiveness as a simple and direct diagnostic tool for ecologists to assess ecosystem complexity and their applicability to the analysis of symbolic sequences (Section 5.5).
