Numerical integration via integrate. In case integrate
fails a Gauss-Legendre quadrature is performed.
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 DiagnosticClass
print(x, what, withNonShows = FALSE, xname, ...)
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.
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 limit of integration. Can be -Inf.
upper limit of integration. Can be Inf.
the maximum number of subintervals.
relative accuracy requested.
absolute accuracy requested.
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.
object of class UnivariateDistribution.
order of Gauss-Legendre quadrature.
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.
the item for which the diagnostic is to be shown.
a character vector with all the diagnostic items to be selected/shown. If empty or missing all items are selected/shown.
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).
an optional name for the diagnostic object to be shown.
should the diagnostic information be reorganized
(using internal function .reorganizeDiagnosticList?
Matthias Kohl Matthias.Kohl@stamats.de
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.
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.
integrate, GLIntegrate,
distrExOptions
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)
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