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The distribution of values in decreasing order of rank is often of interest when values vary widely in scale; this is the rank-size distribution (or rank-frequency distribution), for example for city sizes or word frequencies. These often follow a power law. Some ranks can have non-integer values for tied data values.
In this section we show that the order statistics of the uniform distribution on the unit interval have marginal distributions belonging to the beta distribution family. We also give a simple method to derive the joint distribution of any number of order statistics, and finally translate these results to arbitrary continuous distributions using ...
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 mathematical statistics, the concept has been formalized as the Zipfian distribution: A family of related discrete probability distributions whose rank-frequency distribution is an inverse power law relation. They are related to Benford's law and the Pareto distribution.
In competition ranking, items that compare equal receive the same ranking number, and then a gap is left in the ranking numbers. The number of ranking numbers that are left out in this gap is one less than the number of items that compared equal. Equivalently, each item's ranking number is 1 plus the number of items ranked above it.
From January 2008 to December 2012, if you bought shares in companies when Jeffrey S. Berg joined the board, and sold them when he left, you would have a 47.8 percent return on your investment, compared to a -2.8 percent return from the S&P 500.
Rank-ordering of the population of countries follows a stretched exponential distribution [1] except in the cases of the two "kings": China and India.. In statistics, economics, and econophysics, the king effect is the phenomenon in which the top one or two members of a ranked set show up as clear outliers.
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