Category: Power laws

Zipf's law
Zipf's law (/zɪf/, German: [ts͡ɪpf]) is an empirical law formulated using mathematical statistics that refers to the fact that for many types of data studied in the physical and social sciences, the r
Stefan–Boltzmann law
The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. Specifically, the Stefan–Boltzmann law states that the total energy radiated per unit surface area
Zipf–Mandelbrot law
In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution. Also known as the Pareto–Zipf law, it is a power-law distribution on ranked data, named after the
Hack's law
Hack's law is an empirical relationship between the length of streams and the area of their basins. If L is the length of the longest stream in a basin, and A is the area of the basin, then Hack's law
Kleiber's law
Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the 3⁄4 power of the ani
Cauchy distribution
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauc
Landau distribution
In probability theory, the Landau distribution is a probability distribution named after Lev Landau.Because of the distribution's "fat" tail, the moments of the distribution, like mean or variance, ar
Lévy distribution
In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable. In spectroscopy, this distribution, wit
Simon model
In applied probability theory, the Simon model is a class of stochastic models that results in a power-law distribution function. It was proposed by Herbert A. Simon to account for the wide range of e
Stevens's power law
Stevens' power law is an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the
Gamma correction
Gamma correction or gamma is a nonlinear operation used to encode and decode luminance or tristimulus values in video or still image systems. Gamma correction is, in the simplest cases, defined by the
Generalized Pareto distribution
In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three para
Holtsmark distribution
The (one-dimensional) Holtsmark distribution is a continuous probability distribution. The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parame
Power law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of
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 parame
Pareto distribution
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto (Italian: [paˈreːto] US: /pəˈreɪtoʊ/ pə-RAY-toh), is a power-law probability distribution th
Stable count distribution
In probability theory, the stable count distribution is the conjugate prior of a one-sided stable distribution. This distribution was discovered by Stephen Lihn (Chinese: 藺鴻圖) in his 2017 study of dai
Spectral dimension
The spectral dimension is a real-valued quantity that characterizes a spacetime geometry and topology. It characterizes a spread into space over time, e.g. a ink drop diffusing in a water glass or the