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

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

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

an empirical distribution function (commonly also called an empirical cumulative distribution function, eCDF) is the distribution function associated with...

variables, the joint distribution, as a particular multivariate distribution, may be expressed by a multivariate cumulative distribution function, or by a multivariate...

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

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

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

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

probability density function over that interval. An alternative description of the distribution is by means of the cumulative distribution function, which describes...

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

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

between −1 and 1. These functions are commonly used as activation functions in artificial neurons and as cumulative distribution functions in statistics. The...

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

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

\end{aligned}}} which is equivalent to the cumulative distribution function of the F-distribution: F ( k ; n , p ) = F F -distribution ( x = 1 − p p k + 1 n − k ; d...

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

his original papers describing the distribution. The cumulative distribution function of the Gumbel distribution is F ( x ; μ , β ) = e − e − ( x − μ...

compared to the standard normal distribution (blue). Previous plots shown in green. The cumulative distribution function (CDF) can be written in terms of...

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

function, and cumulative distribution function. The two words cumulative and density contradict each other. The value of a density function in an interval about...

)={\frac {f(x/\beta ;\alpha ,1)}{\beta }}} The cumulative distribution function is the regularized gamma function F ( x ; α , β ) = Γ ( α , β x ) Γ ( α ) =...

model the distribution of wealth, then the parameter α is called the Pareto index. From the definition, the cumulative distribution function of a Pareto...

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...

Laplace distribution is easy to integrate (if one distinguishes two symmetric cases) due to the use of the absolute value function. Its cumulative distribution...

{\displaystyle k} . Tables of the chi-squared cumulative distribution function are widely available and the function is included in many spreadsheets and all...

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

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

integrals involving δ. In this context, the Heaviside function is the cumulative distribution function of a random variable which is almost surely 0. (See...

tractability in posterior distribution computations. The probability density and cumulative distribution functions of the gamma distribution vary based on the...