Rgamma {UCS}R Documentation

The Regularized Gamma Function (sfunc)

Description

Computes the regularized Gamma function and its inverse. Both the lower and the upper regularized Gamma function are supported, and the Gamma value can be scaled to a base 10 logarithm.

Usage

Rgamma(a, x, lower=TRUE, log=FALSE)

Rgamma.inv(a, y, lower=TRUE, log=FALSE)

Arguments

a a non-negative numeric vector, the parameter of the incomplete Gamma function
x a non-negative numeric vector, the point at which the incomplete Gamma function is evaluated
y a numeric vector, the values of the regularized Gamma function (or their base 10 logarithms if log=TRUE)
lower if TRUE, computes the lower regularized Gamma function (default). Otherwise, computes the upper regularized Gamma function.
log if TRUE, the Gamma values are base 10 logarithms (default: FALSE)

Details

The regularized Gamma functions scale the corresponding incomplete Gamma functions to the interval [0,1], by dividing through Γ(a). Thus, the lower regularized Gamma function is given by

P(a,x) = gamma(a,x) / Gamma(a)

and the upper regularized Gamma function is given by

Q(a,x) = Gamma(a,x) / Gamma(a)

Value

Rgamma returns the (lower or upper) regularized Gamma function with parameter a evaluated at point x.

Rgamma.inv returns the point x at which the (lower or upper) regularized Gamma function with parameter a evaluates to y.

See Also

Cgamma, Igamma, Cbeta, Ibeta, Rbeta

Examples

## P(X >= k) for Poisson distribution with mean alpha
alpha <- 5
k <- 10
Rgamma(k, alpha) # == ppois(k-1, alpha, lower=FALSE)
[Package UCS version 0.5 Index]