# Category: Functions related to probability distributions

Error function
In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: This integral is a special (non-elementary) sig
Fragmentation function
In a sufficiently hard interaction between particles, the cross section can be factorized into parton distribution functions (PDFs), the hard scattering part, and fragmentation functions. The fragment
Ogive (statistics)
In statistics, an ogive, also known as a cumulative frequency polygon, can refer to one of two things: * any hand drawn graphic of a cumulative distribution function * any empirical cumulative distr
Distortion function
A distortion function in mathematics and statistics, for example, , is a non-decreasing function such that and . The dual distortion function is . Distortion functions are used to define distortion ri
Hazard function
No description available.
Q-function
In statistics, the Q-function is the tail distribution function of the standard normal distribution. In other words, is the probability that a normal (Gaussian) random variable will obtain a value lar
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
Quantile function
In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the varia
Empirical characteristic function
Let be independent, identically distributed real-valued random variables with common characteristic function . The empirical characteristic function (ECF) defined as is an unbiased and consistent esti
Marcum Q-function
In statistics, the generalized Marcum Q-function of order is defined as where and and is the modified Bessel function of first kind of order . If , the integral converges for any . The Marcum Q-functi
Probability-generating function
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random varia
Probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possib
Cumulative distribution function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable , or just distribution function of , evaluated at , is the probability that will take
Characteristic function (probability theory)
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density
Owen's T function
In mathematics, Owen's T function T(h, a), named after statistician Donald Bruce Owen, is defined by The function was first introduced by Owen in 1956.