ncg (version 0.1.1)

pgammanc: Computes the cumulative distribution function of the noncentral gamma function

Description

Computes the cumulative distribution function of the noncentral gamma function: $$I_x(\alpha, \delta) = P(X\le x)= \sum_{i=0}^\infty \frac{e^{-\delta/2}(\delta/2)^i}{i!} I_x(\alpha+i)$$ where $I_x(\alpha)$ is the central incomplete gamma function, $\alpha>0$, $\delta>0$, $x\ge 0$.

Usage

pgammanc(x, alpha, delta)

Arguments

x

a vector of positive quantiles.

alpha

a vector of the noncentral gamma parameter, alpha > 0.

delta

a vector of the noncentrality parameter, delta > 0.

References

Oliveira, IRC; Ferreira, DF Computing the noncentral gamma distribution, its inverse and the noncentrality parameter. Computational Statistics. Submmited for publications. 2012.

See Also

Package homepage:

Examples

library(ncg)
x <- c(2, 3, 2)
alpha <- c(1.1, 3.0, 9.0)
delta <- c(1.8, 2.3, 0.5)
pgammanc(x, alpha, delta)
# single values example
pgammanc(2, 2, 0.5)