distrExIntegrate {distrEx}

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, ..., diagnostic = FALSE)
showDiagnostic(x, what, withNonShows = FALSE, ...)
getDiagnostic(x, what, reorganized=TRUE)
## S3 method for class 'DiagnosticClass'
print(x, what, withNonShows = FALSE, xname, ...)

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.

diagnostic

logical; if TRUE, the return value obtains an attribute "diagnostic" with diagnostic information on the integration, i.e., a list with entries method ("integrate" or "GLIntegrate"), call, result (the complete return value of the method), args (the args with which the method was called), and time (the time to compute the integral).

...

In case of integrators: additional arguments to be passed to f. Remember to use argument names not matching those of integrate and GLIntegrate! In case of showDiagnostic, print.DiagnosticClass: additional arguments to be passed on to print methods called for particular items in the diagnostic list.

x

the item for which the diagnostic is to be shown.

what

a character vector with all the diagnostic items to be selected/shown. If empty or missing all items are selected/shown.

withNonShows

internally we distinguish items which are easily printed (first kind) (numeric, logical, character) and more difficult ones (second kind), e.g., calls, functions, lists. The distinction is made according to the list item name. If withNonShows==TRUE one also attempts to show the selected items of the second kind, otherwise they are not shown (but returned).

xname

an optional name for the diagnostic object to be shown.

reorganized

should the diagnostic information be reorganized (using internal function .reorganizeDiagnosticList?

Details

distrExIntegrate 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.

distrExIntegrate is called from many places in the distr and robast families of packages. At every such instance, diagnostic information can be collected (setting a corresponding argument diagnostic to TRUE in the calling function. This diagnostic information is originally stored in a tree like list structure of S3 class DiagnosticClass which is then attached as attribute diagnostic to the respective object. It can be inspected and accessed through showDiagnostic and getDiagnostic. More specifically, for any object with attribute diagnostic, showDiagnostic shows the diagnostic collected during integration, and getDiagnostic returns the diagnostic collected during integration. To this end, print.DiagnosticClass is an S3 method for print for objects of S3 class DiagnosticClass.

Value

The value of distrExIntegrate is a numeric approximation of the integral. If argument diagnostic==TRUE in distrExIntegrate, the return value has an attribute diagnostic of S3 class DiagnosticClass containing diagnostic information on the integration.

showDiagnostic, getDiagnostic, print.DiagnosticClass all return (invisibly) a list with the selected items, reorganized by internal function .reorganizeDiagnosticList, respectively, in case of argument reorganized==FALSE, getDiagnostic returns (invisibly) the diagnostic information as is.

Author(s)

Matthias Kohl [e-mail]

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.

See Also

integrate, GLIntegrate, distrExOptions

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)