Returns the cumulative distribution function for a distribution evaluated at a given point.

cdf(object, x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)

## Arguments

object Distribution. vector of numerics to evaluate function at. additional arguments. logical; if TRUE (default), probabilities are $$P(X \le x)$$ otherwise, $$P(X > x)$$. logical; if TRUE, probabilities p are given as log(p). if TRUE (default) returns results in simplest form (vector or data.table) otherwise as data.table.

## Value

Cumulative distribution function evaluated at given points as either a numeric if simplify is TRUE or as a data.table.

## Details

The (lower tail) cumulative distribution function, $$F_X$$, is defined as $$F_X(x) = P(X \le x)$$ If lower.tail is FALSE then $$1 - F_X(x)$$ is returned, also known as the survival function.

If available a cdf will be returned without warning using an analytic expression. Otherwise, if the distribution has not been decorated with FunctionImputation, NULL is returned. To impute the cdf, use decorate(distribution, FunctionImputation), this will provide a numeric calculation for the cdf with warning.

Additional named arguments can be passed, which are required for composite distributions such as ProductDistribution and ArrayDistribution.

## R6 Usage

\$cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)

pdf, quantile, rand for other statistical functions. FunctionImputation, decorate for imputing missing functions.