Rank-size distribution
（重定向自Rank Size Rule）
![Rank-size distribution of the population of countries follows a stretched exponential distribution[1] except in the cases of the two](/Images/godic/202502/06/Rank_order_countries4317.png"){kind=icon}
![Wikipedia word frequency plot, showing three segments with distinct behavior.](/Images/godic/202502/06/Wikipedia-n-zipf4317.png")
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.