Publication

Scale-free behavior and universality in random fragmentation and aggregation

2004
Journal Articles

Abstract

Two distinct methods underlying the existence of power-law distribution were studied. The distribution ws stationary under the process of merging and splitting of classes and the distribution of the entities under study was invariant. An explanation for the ubiquitous inverse n relationship in the species abundance relationship in ecology and 1/n2 distribution of company size was also proposed. It was found that the successive splitting and mergers and principle of invariance under recategorization both leads to power law distributions.

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2004
Journal Articles

Abstract

Official source

Related concepts (31)

Normal distribution

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.

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.

Poisson distribution

In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.

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Scale-free behavior and universality in random fragmentation and aggregation

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