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

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

object | Distribution. |
---|---|

x1 | vector of numerics to evaluate function at. |

... | additional arguments. |

lower.tail | logical; if TRUE (default), probabilities are \(P(X \le x)\) otherwise, \(P(X > x)\). |

log.p | logical; if TRUE, probabilities p are given as log(p). |

simplify | if TRUE (default) returns results in simplest form (vector or data.table) otherwise as data.table. |

Cumulative distribution function evaluated at given points as either a numeric if `simplify`

is TRUE
or as a data.table.

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`

.

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

`pdf`

, `quantile`

, `rand`

for other statistical functions.
`FunctionImputation`

, `decorate`

for imputing missing functions.