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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 ...
In the parabolic fractal distribution, the logarithm of the frequency is a quadratic polynomial of the logarithm of the rank. This can markedly improve the fit over a simple power-law relationship. [36] Like fractal dimension, it is possible to calculate Zipf dimension, which is a useful parameter in the analysis of texts. [37]
RA calculator: Software for calculating the ratio of areas (RA) in a rank-size plot (also see [8]). HT 2.0 calculator: An excel sheet calculator which calculates both head/tail breaks 1.0 and head/tail breaks 2.0 with a version for smaller datasets and a version for very large (binned) datasets.
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.. For example, if the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively.
If F(r) is the Fisher transformation of r, the sample Spearman rank correlation coefficient, and n is the sample size, then z = n − 3 1.06 F ( r ) {\displaystyle z={\sqrt {\frac {n-3}{1.06}}}F(r)} is a z -score for r , which approximately follows a standard normal distribution under the null hypothesis of statistical independence ( ρ = 0 ).
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A primate city distribution is a rank-size distribution that has one very large city with many much smaller cities and towns and no intermediate-sized urban centers, creating a statistical king effect. [3] The law of the primate city was first proposed by the geographer Mark Jefferson in 1939. [4]
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