RobExtremes (version 1.3.2)

E: Generic Function for the Computation of (Conditional) Expectations

Description

Generic function for the computation of (conditional) expectations.

Usage

E(object, fun, cond, ...)
# S4 method for GEV,missing,missing
E(object, low = NULL, upp = NULL, ..., diagnostic = FALSE)
# S4 method for DistributionsIntegratingByQuantiles,function,missing
E(object,
         fun, low = NULL, upp = NULL,
         rel.tol= getdistrExOption("ErelativeTolerance"),
         lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),
         upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),
         IQR.fac = max(1e4,getdistrExOption("IQR.fac")), ..., diagnostic = FALSE)
# S4 method for Gumbel,missing,missing
E(object, low = NULL, upp = NULL, ..., diagnostic = FALSE)
# S4 method for GPareto,missing,missing
E(object, low = NULL, upp = NULL, ..., diagnostic = FALSE)
# S4 method for GPareto,function,missing
E(object, fun, low = NULL, upp = NULL,
             rel.tol= getdistrExOption("ErelativeTolerance"),
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),
             IQR.fac = max(1e4,getdistrExOption("IQR.fac")), ..., diagnostic = FALSE)
# S4 method for Pareto,missing,missing
E(object, low = NULL, upp = NULL, ..., diagnostic = FALSE)

Value

The expectation is computed.

Arguments

object

object of class "Distribution"

fun

if missing the (conditional) expectation is computed else the (conditional) expection of fun is computed.

cond

if not missing the conditional expectation given cond is computed.

rel.tol

relative tolerance for distrExIntegrate.

low

lower bound of integration range.

upp

upper bound of integration range.

lowerTruncQuantile

lower quantile for quantile based integration range.

upperTruncQuantile

upper quantile for quantile based integration range.

IQR.fac

factor for scale based integration range (i.e.; median of the distribution \(\pm\)IQR.fac\(\times\)IQR).

...

additional arguments to fun

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).

Methods

object = "Gumbel", fun = "missing", cond = "missing":

exact evaluation using explicit expressions.

object = "GPareto", fun = "missing", cond = "missing":

exact evaluation using explicit expressions.

object = "DistributionsIntegratingByQuantiles", fun = "function", cond = "missing":

use probability transform, i.e., a substitution y = p(object)(x) for numerical integration.

object = "GPareto", fun = "function", cond = "missing":

use substitution method (y := log(x)) for numerical integration.

object = "Pareto", fun = "missing", cond = "missing":

exact evaluation using explicit expressions.

Author

Matthias Kohl and Peter Ruckdeschel

Details

The precision of the computations can be controlled via certain global options; cf. distrExOptions. Also note that arguments low and upp should be given as named arguments in order to prevent them to be matched by arguments fun or cond. Also the result, when arguments low or upp is given, is the unconditional value of the expectation; no conditioning with respect to low <= object <= upp is done. To be able to use integration after transformation via the respective probability transformation to [0,1], we introduce a class union "DistributionsIntegratingByQuantiles", which currently comprises classes "GPareto", "Pareto", "Weibull", "GEV". In addition, the specific method for "GPareto", "function", "missing" uses integration on [0,1] via the substitution method (y := log(x)).

Diagnostics on the involved integrations are available if argument diagnostic is TRUE. Then there is attribute diagnostic attached to the return value, which may be inspected and accessed through showDiagnostic and getDiagnostic.

See Also

distrExIntegrate, m1df, m2df, Distribution-class

Examples

GP <- GPareto(shape=0.3)

E(GP)
E(GP, fun = function(x){2*x^2}) ## uses the log trafo

P <- Pareto()
E(P)
E(P,fun = function(x){1/(x^2+1)})