Rank-size distribution is the distribution of size by rank, in decreasing order of size. For example, if a data set consists of items of sizes 5, 100, 5, and 8, the rank-size distribution is 100, 8, 5, 5 (ranks 1 through 4). This is also known as the
rank-frequency distribution, when the source data are from a
frequency distribution. These are particularly of interest when the data vary significantly in scale, such as city size or word frequency. These distributions frequently follow a
power law distribution, or less well-known ones such as a
stretched exponential function or
parabolic fractal distribution, at least approximately for certain ranges of ranks; see below.