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...

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)...

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

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

\\[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...

The phrase cumulative density function could mean cumulative distribution function or probability density function. This disambiguation page lists articles...

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

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

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

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

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 ;...

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

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

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

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

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

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...

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...

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

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...

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

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

probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density function if it exists)...

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

mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic...

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

(-iz)=\operatorname {erfcx} (-iz).} The error function is essentially identical to the standard normal cumulative distribution function, denoted Φ, also named norm(x)...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...