Function DistributionCumulative(distribution, x)

# DistributionCumulative

The function DistributionCumulative computes the cumulative probability value of a given distribution.

DistributionCumulative(
distribution,            ! (input) distribution
x                        ! (input) numerical expression
)


## Arguments

distribution

An expression representing any distribution (such as Normal(0,1)).

x

A scalar numerical expression.

## Return Value

The function CumulativeDistribution(distribution,$$x$$), for $$x\in(-\infty,\infty)$$ returns the probability $$P(X\leq x)$$ where the stochastic variable $$X$$ is distributed according to the given distribution.

Note

For continuous distributions AIMMS can compute the derivatives of the cumulative and inverse cumulative distribution functions. As a consequence, you may use these functions in the constraints of a nonlinear model when the second argument is a variable.

The function DistributionInverseCumulative. The function DistributionCumulative is discussed in full detail in Discrete Distributions of the Language Reference.