Rank-size distribution in the context of Frequency distribution

Rank-size distribution in the context of Frequency distribution

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⭐ Core Definition: Rank-size distribution

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 scales, 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.

A rank-size distribution is not a probability distribution or cumulative distribution function. Rather, it is a discrete form of a quantile function (inverse cumulative distribution) in reverse order, giving the size of the element at a given rank.

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Rank-size distribution in the context of Primate city

A primate city is a city that is the largest in its country, province, state, or region, and disproportionately larger than any others in the urban hierarchy. 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.

The law of the primate city was first proposed by the geographer Mark Jefferson in 1939. He defines a primate city as being "at least twice as large as the next largest city and more than twice as significant." Aside from size and population, a primate city will usually have precedence in all other aspects of its country's society such as economics, politics, culture, and education. Primate cities also serve as targets for the majority of a country or region's internal migration.

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← Primate city
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Stretched exponential function → King effect → China → India → Frequency distribution → Power law → Parabolic fractal distribution → Probability distribution → Cumulative distribution function → Quantile function →