The Rank-Size Rule of City Populations. The rank-size rule (or rank-size distribution) of city populations, is a commonly observed statistical relationship between the population sizes and population ranks of a nation's cities. Keywords: Rank-Size Rule, Zipf's Law, Primacy Index, Primate City . and E-2) which represents the theoretical size distribution of urban centres of the study. The best known effort to create such a hierarchy is the rank-size rule developed by G.K. Zipf in At its most basic, the Zipf's formula is as follows: Pr=P1/P2 n where Pr= the population of the rth city, P1 = the population of the largest city, and r = the size rank of the rth city in the set.


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This however does not always account for the immense populations of metropolitan areas such as London, Paris, New York, Los Angeles, Moscow, and Shanghai.

For this reason, inBrian Berry attempted to evaluate city-size variations and distributions by comparing 37 countries. As a result of his research, he found that thirteen nations exhibited rank-size distributions, fifteen nations exhibited primate distributions one very large city rank size rule theory many smaller centers around itand nine countries had intermediate distributions a number of intermediate cities.

The Rank-Size Rule of City Populations

The relationship between population size and population rank is inherently negative. Growth rates are independent of city rank size rule theory or at least weakly related and absolute growth is roughly proportional to city size.

It has also been show to fit city population versus rank better. All are real-world observations that follow power lawssuch as Zipf's lawthe Yule distributionor the Pareto distribution.

The Rank Size Rule According to Zipf

If one ranks the population size of cities in a given country or in the entire world and calculates rank size rule theory natural logarithm of the rank and of the city population, the resulting graph will show a log-linear pattern. When presented with a ranking of data, is the rank size rule theory variable approximately one-third the value of the highest-ranked one?

Or, conversely, is the highest-ranked variable approximately ten times the value of the tenth-ranked one? If so, the rank size rule has possibly helped spot another power law relationship.

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Known exceptions to simple rank-size distributions[ edit ] While Zipf's law works well in many cases, it tends to not fit the largest cities in many countries; one type rank size rule theory deviation is known as the King effect. A study found that Zipf's law was rejected for 53 of 73 countries, far more rank size rule theory would be expected based on random chance.

For instance, in the United Statesalthough its largest city, New York Cityhas more than twice the population of second-place Los Angelesthe two cities' metropolitan areas also the two largest in the country are much closer in population. In metropolitan-area population, New York City is only 1.


In other countries, the largest city would dominate much more than expected. City size and education expenditure. City size and cost of living. City size and public recreation City size and retail facilities City size and family life.

Rank-size distribution - Wikipedia

City size and miscellaneous rank size rule theory and social characteristics of urban life community participation, social contentment.

City size and rank size rule theory. He found that the distributions fall into two major categories namely the Rank Size Distribution and the Primate Distribution.

Thirteen of the thirty-eight countries had log-normally distributed sizes. The primate distribution which was characteristics of fifteen out of thirty-eight countries examined is observed, when a stratum of small towns and cities is dominated by one or more very large cities and there are deficiencies in the number of cities of intermediate size.