statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle...

quantile function of a distribution is the inverse of the cumulative distribution function. The quantile function of the standard normal distribution is called...

the cumulative distribution function or c.d.f.) or inverse distribution function. With reference to a continuous and strictly increasing cumulative distribution...

expressed in terms of a joint cumulative distribution function and either in terms of a joint probability density function (in the case of continuous variables)...

\\[2pt]0&{\text{otherwise}}.\end{cases}}} The cumulative distribution function of the continuous uniform distribution is: F ( x ) = { 0 for  x < a , x − a b...

statistics, an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the distribution function associated with the...

statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in...

parameter, and c {\displaystyle c} is the scale parameter. The cumulative distribution function is F ( x ; μ , c ) = erfc ⁡ ( c 2 ( x − μ ) ) = 2 − 2 Φ ( c...

equivalent to the cumulative distribution functions of the beta distribution and of the F-distribution: F ( k ; n , p ) = F beta-distribution ( x = 1 − p ;...

density functions or cumulative distribution functions. There are particularly simple results for the characteristic functions of distributions defined...

Distribution function may refer to Cumulative distribution function, a basic concept of probability theory Distribution function (physics), a function...

probability distribution can be described in various forms, such as by a probability mass function or a cumulative distribution function. One of the most...

cumulative distribution function of the lifetime. Sometimes complementary cumulative distribution functions are called survival functions in general. Let the...

refer to the cumulative distribution function (CDF), or it may be a probability mass function (PMF) rather than the density. Density function itself is also...

hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution. Certain values...

{1}{\pi \gamma }}.\!} The Cauchy distribution is the probability distribution with the following cumulative distribution function (CDF): F ( x ; x 0 , γ ) =...

distribution; another is the arctan function, which is related to the cumulative distribution function of a Cauchy distribution. A sigmoid function is...

vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can be computed with the numerical...

{\displaystyle \varphi } be respectively the cumulative probability distribution function and the probability density function of the N ( 0 , 1 ) {\displaystyle...

continuous probability distribution that has a constant failure rate. The quantile function (inverse cumulative distribution function) for Exp(λ) is F − 1...

that the Voigt distributions are also closed under convolution. Using the above definition for z , the cumulative distribution function (CDF) can be found...

The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function. This distribution has neither a...

parameter of the distribution. Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to...

y\in [c,d]} . Finding the marginal cumulative distribution function from the joint cumulative distribution function is easy. Recall that: For discrete...

density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined...

parameter m (the minimum) and a scale parameter s > 0 with the cumulative distribution function   Pr (   X ≤ x   ) = exp ⁡ [   − (   x − m   s ) − α   ]  ...

in shape to the log-normal distribution but has heavier tails. Unlike the log-normal, its cumulative distribution function can be written in closed form...

differently (Gompertz–Makeham law of mortality). The cumulative distribution function of the Gompertz distribution is: F ( x ; η , b ) = 1 − exp ⁡ ( − η ( e b...

statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the...

continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution. For...