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The rank-size rule is a common standard by which urban primacy is established. A distribution such as that in the United States or China does not exhibit a pattern of primacy, but countries with a dominant "primate city" clearly vary from the rank-size rule in the opposite manner. Therefore, the rule helps to classify national (or regional ...
For example, when corporations are ranked by decreasing size, their sizes are found to be inversely proportional to the rank. [13] The same relation is found for personal incomes (where it is called Pareto principle [ 14 ] ), number of people watching the same TV channel, [ 15 ] notes in music, [ 16 ] cells transcriptomes , [ 17 ] [ 18 ] and more.
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]
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.
The distribution of words ranked by their frequency in a random text corpus is approximated by a power-law distribution, known as Zipf's law.. If one plots the frequency rank of words contained in a moderately sized corpus of text data versus the number of occurrences or actual frequencies, one obtains a power-law distribution, with exponent close to one (but see Powers, 1998 and Gelbukh ...
Probability density functions of the order statistics for a sample of size n = 5 from an exponential distribution with unit scale parameter. In statistics, the kth order statistic of a statistical sample is equal to its kth-smallest value. [1]
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 ).
The urban hierarchy ranks each city based on the size of population residing within the nationally defined statistical urban area. Because urban population depends on how governments define their metropolitan areas, urban hierarchies are conventionally ranked at the national level; however, the ranking can be extended globally to include all cities.