Concept
Zipf's law
Related concepts (15)
Power law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to a power of the change, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.
Pareto principle
The Pareto principle states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few"). Other names for this principle are the 80/20 rule, the law of the vital few, or the principle of factor sparsity. Management consultant Joseph M. Juran developed the concept in the context of quality control and improvement after reading the works of Italian sociologist and economist Vilfredo Pareto, who wrote about the 80/20 connection while teaching at the University of Lausanne.
Pareto distribution
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population.
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.
Long tail
In statistics and business, a long tail of some distributions of numbers is the portion of the distribution having many occurrences far from the "head" or central part of the distribution. The distribution could involve popularities, random numbers of occurrences of events with various probabilities, etc. The term is often used loosely, with no definition or an arbitrary definition, but precise definitions are possible. In statistics, the term long-tailed distribution has a narrow technical meaning, and is a subtype of heavy-tailed distribution.
Stable distribution
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
Harmonic series (mathematics)
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a divergent series. Its divergence was proven in the 14th century by Nicole Oresme using a precursor to the Cauchy condensation test for the convergence of infinite series.
Menzerath's law
Menzerath's law, or Menzerath–Altmann law (named after Paul Menzerath and Gabriel Altmann), is a linguistic law according to which the increase of the size of a linguistic construct results in a decrease of the size of its constituents, and vice versa. E.g., the longer a sentence (measured in terms of the number of clauses) the shorter the clauses (measured in terms of the number of words), or: the longer a word (in syllables or morphs) the shorter the syllables or morphs in sounds.
Harmonic number
In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: Starting from n = 1, the sequence of harmonic numbers begins: Harmonic numbers are related to the harmonic mean in that the n-th harmonic number is also n times the reciprocal of the harmonic mean of the first n positive integers. Harmonic numbers have been studied since antiquity and are important in various branches of number theory.
Heaps' law
In linguistics, Heaps' law (also called Herdan's law) is an empirical law which describes the number of distinct words in a document (or set of documents) as a function of the document length (so called type-token relation). It can be formulated as where VR is the number of distinct words in an instance text of size n. K and β are free parameters determined empirically. With English text corpora, typically K is between 10 and 100, and β is between 0.4 and 0.6. The law is frequently attributed to Harold Stanley Heaps, but was originally discovered by .