generalized K-distribution is a three-parameter family of continuous probability distributions. The distribution arises by compounding two gamma distributions. In...

chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use: With a shape parameter k and a...

number of events. When k = 1 {\displaystyle k=1} , the distribution simplifies to the exponential distribution. The Erlang distribution is a special case of...

explicitly. The geometric distribution gives the probability that the first occurrence of success requires k {\displaystyle k} independent trials, each...

Poisson distribution is Pr ( X 1 = k 1 , X 2 = k 2 ) = exp ⁡ ( − λ 1 − λ 2 − λ 3 ) λ 1 k 1 k 1 ! λ 2 k 2 k 2 ! ∑ k = 0 min ( k 1 , k 2 ) ( k 1 k ) ( k 2 k )...

chi-squared distribution (also chi-square or χ 2 {\displaystyle \chi ^{2}} -distribution) with k {\displaystyle k} degrees of freedom is the distribution of a...

theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in...

multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a k-sided dice...

one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if...

statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of k {\displaystyle k} successes (random draws...

where ( n k ) = n ! k ! ( n − k ) ! {\displaystyle {\binom {n}{k}}={\frac {n!}{k!(n-k)!}}} is the binomial coefficient, hence the distribution's name. The...

theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable...

in describing the distribution, (e.g. 1 to K). The K-dimensional categorical distribution is the most general distribution over a K-way event; any other...

series distribution Log(p), with probability mass function f ( k ; r , p ) = − p k k ln ⁡ ( 1 − p ) , k ∈ N . {\displaystyle f(k;r,p)={\frac {-p^{k}}{k\ln(1-p)}}...

simply F ( k ; a , b ) = ⌊ k ⌋ − a + 1 b − a + 1 {\displaystyle F(k;a,b)={\frac {\lfloor k\rfloor -a+1}{b-a+1}}} on the distribution's support k ∈ [ a ,...

particle size distribution. The probability density function of a Weibull random variable is f ( x ; λ , k ) = { k λ ( x λ ) k − 1 e − ( x / λ ) k , x ≥ 0 ...

variable obeying a chi-squared distribution. If Z 1 , … , Z k {\displaystyle Z_{1},\ldots ,Z_{k}} are k {\displaystyle k} independent, normally distributed...

system. The distribution is expressed in the form: p i ∝ exp ⁡ ( − ε i k T ) {\displaystyle p_{i}\propto \exp \left(-{\frac {\varepsilon _{i}}{kT}}\right)}...

this distribution, over possible outcomes k, is f ( k ; p ) = { p if  k = 1 , q = 1 − p if  k = 0. {\displaystyle f(k;p)={\begin{cases}p&{\text{if }}k=1...

_{i=1}^{K}x_{i}^{\alpha _{i}-1}} where { x k } k = 1 k = K {\displaystyle \{x_{k}\}_{k=1}^{k=K}} belong to the standard K − 1 {\displaystyle K-1} simplex...

one-dimensional probability distributions that can be used to test whether a sample came from a given reference probability distribution (one-sample K–S test), or to...

Student's t distribution (or simply the t distribution)   t ν   {\displaystyle \ t_{\nu }\ } is a continuous probability distribution that generalizes...

probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in...

continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment...

cumulative distribution function of the univariate degenerate distribution is: F k 0 ( x ) = { 1 , if  x ≥ k 0 0 , if  x < k 0 {\displaystyle F_{k...

is a Mersenne prime. This choice simplifies the primitivity test and k-distribution test that are needed in the parameter search. The series x {\displaystyle...

probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes...

product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given...

satisfied by the distribution is: 0 = k B T v f ′ ( v ) + f ( v ) ( m v 2 − 2 k B T ) , f ( 1 ) = 2 π [ m k B T ] 3 / 2 exp ⁡ ( − m 2 k B T ) ; {\displaystyle...

Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f (...