R: Integration of One-Dimensional Functions

distrExIntegrate {distrEx}

R Documentation

Integration of One-Dimensional Functions

Description

Numerical integration via integrate. In case integrate fails a Gauss-Legendre quadrature is performed.

Usage

distrExIntegrate(f, lower, upper, subdivisions = 100, 
                 rel.tol = .Machine$double.eps^0.25, 
                 abs.tol = rel.tol, stop.on.error = TRUE, 
                 distr, order, ...)

Arguments

`f`	an R function taking a numeric first argument and returning a numeric vector of the same length. Returning a non-finite element will generate an error.
`lower`	lower limit of integration. Can be `-Inf`.
`upper`	upper limit of integration. Can be `Inf`.
`subdivisions`	the maximum number of subintervals.
`rel.tol`	relative accuracy requested.
`abs.tol`	absolute accuracy requested.
`stop.on.error`	logical. If `TRUE` (the default) an error stops the function. If false some errors will give a result with a warning in the `message` component.
`distr`	object of class `UnivariateDistribution`.
`order`	order of Gauss-Legendre quadrature.
`...`	additional arguments to be passed to `f`. Remember to use argument names not matching those of `integrate` and `GLIntegrate`!

Details

This function calls integrate. In case integrate returns an error a Gauss-Legendre integration is performed using GLIntegrate. If lower or (and) upper are infinite the GLIntegrateTruncQuantile, respectively the 1-GLIntegrateTruncQuantile quantile of distr is used instead.

Value

Estimate of the integral.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

Based on QUADPACK routines dqags and dqagi by R. Piessens and E. deDoncker-Kapenga, available from Netlib.

R. Piessens, E. deDoncker-Kapenga, C. Uberhuber, D. Kahaner (1983) Quadpack: a Subroutine Package for Automatic Integration. Springer Verlag.

W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery (1992) Numerical Recipies in C. The Art of Scientific Computing. Second Edition. Cambridge University Press.

Examples

fkt <- function(x){x*dchisq(x+1, df = 1)}
integrate(fkt, lower = -1, upper = 3)
GLIntegrate(fkt, lower = -1, upper = 3)
try(integrate(fkt, lower = -1, upper = 5))
distrExIntegrate(fkt, lower = -1, upper = 5)

[Package distrEx version 2.7.0 Index]