distrEx (version 2.6)

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

Description

Generic function for the computation of (conditional) expectations.

Usage

E(object, fun, cond, ...)
"E"(object,  low = NULL, upp = NULL, Nsim = getdistrExOption("MCIterations"), ...)
"E"(object, fun,  useApply = TRUE, low = NULL, upp = NULL, Nsim = getdistrExOption("MCIterations"), ...)
"E"(object, fun, useApply = TRUE, low = NULL, upp = NULL,  rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, low = NULL,  upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, fun, useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, cond, low = NULL,  upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, fun, cond, useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, fun, useApply = TRUE,  low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object,  Nsim = getdistrExOption("MCIterations"), ...)
"E"(object, fun, useApply = TRUE, Nsim = getdistrExOption("MCIterations"), ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, fun,  useApply = TRUE, ...)
"E"(object, cond, useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, cond, useApply = TRUE, low = NULL, upp = NULL, ...)
"E"(object, fun, cond,  withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL, Nsim = getdistrExOption("MCIterations"), ...)
"E"(object, fun, cond,  withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac") , ...)
"E"(object, fun, cond,  withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL,...)
"E"(object, fun, cond,  withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL,...) 
"E"(object, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ... )
"E"(object, fun,  useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ... )
"E"(object, cond, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ... )
"E"(object, fun, cond,  useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"),  lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ... )
"E"(object, fun, cond, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),  upperTruncQuantile = getdistrExOption("EupperTruncQuantile"),  IQR.fac = getdistrExOption("IQR.fac"), ... )
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, fun, low = NULL, upp = NULL,  rel.tol = getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), IQR.fac = getdistrExOption("IQR.fac"), ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, fun, low = NULL, upp = NULL,  rel.tol = getdistrExOption("ErelativeTolerance"), lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), IQR.fac = max(10000, getdistrExOption("IQR.fac")), ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)
"E"(object, low = NULL, upp = NULL, ...)

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.

Nsim

number of MC simulations used to determine the expectation.

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 $+-$IQR.fac$*$IQR).

...

additional arguments to fun

useApply

logical: should sapply, respectively apply be used to evaluate fun.

withCond

logical: is cond in the argument list of fun.

Value

The (conditional) expectation is computed.

Methods

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

expectation of univariate distributions using crude Monte-Carlo integration.

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

expectation of absolutely continuous univariate distributions using distrExIntegrate.

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

expectation of discrete univariate distributions using support and sum.

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

expectation of multivariate distributions using crude Monte-Carlo integration.

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

expectation of discrete multivariate distributions. The computation is based on support and sum.

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

expectation of univariate Lebesgue decomposed distributions by separate calculations for discrete and absolutely continuous part.

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

expectation of an affine linear transformation $aX+b$ as $a E[X]+b$ for X either "DiscreteDistribution" or "AbscontDistribution".

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

expectation of an affine linear transformation $aX+b$ as $a E[X]+b$ for X either "UnivarLebDecDistribution".

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

expectation of fun under univariate distributions using crude Monte-Carlo integration.

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

expectation of fun under univariate Lebesgue decomposed distributions by separate calculations for discrete and absolutely continuous part.

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

expectation of fun under absolutely continuous univariate distributions using distrExIntegrate.

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

expectation of fun under discrete univariate distributions using support and sum.

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

expectation of multivariate distributions using crude Monte-Carlo integration.

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

expectation of fun under discrete multivariate distributions. The computation is based on support and sum.

object = "UnivariateCondDistribution", fun = "missing", cond = "numeric":

conditional expectation for univariate conditional distributions given cond. The integral is computed using crude Monte-Carlo integration.

object = "AbscontCondDistribution", fun = "missing", cond = "numeric":

conditional expectation for absolutely continuous, univariate conditional distributions given cond. The computation is based on distrExIntegrate.

object = "DiscreteCondDistribution", fun = "missing", cond = "numeric":

conditional expectation for discrete, univariate conditional distributions given cond. The computation is based on support and sum.

object = "UnivariateCondDistribution", fun = "function", cond = "numeric":

conditional expectation of fun under univariate conditional distributions given cond. The integral is computed using crude Monte-Carlo integration.

object = "AbscontCondDistribution", fun = "function", cond = "numeric":

conditional expectation of fun under absolutely continuous, univariate conditional distributions given cond. The computation is based on distrExIntegrate.

object = "DiscreteCondDistribution", fun = "function", cond = "numeric":

conditional expectation of fun under discrete, univariate conditional distributions given cond. The computation is based on support and sum.

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

expectation by separate evaluation of expectation of discrete and abs. continuous part and subsequent weighting.

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

expectation by separate evaluation of expectation of discrete and abs. continuous part and subsequent weighting.

object = "UnivarLebDecDistribution", fun = "missing", cond = "ANY":

expectation by separate evaluation of expectation of discrete and abs. continuous part and subsequent weighting.

object = "UnivarLebDecDistribution", fun = "function", cond = "ANY":

expectation by separate evaluation of expectation of discrete and abs. continuous part and subsequent weighting.

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

expectation is computed component-wise with subsequent weighting acc. to mixCoeff.

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

expectation is computed component-wise with subsequent weighting acc. to mixCoeff.

object = "UnivarMixingDistribution", fun = "missing", cond = "ANY":

expectation is computed component-wise with subsequent weighting acc. to mixCoeff.

object = "UnivarMixingDistribution", fun = "function", cond = "ANY":

expectation is computed component-wise with subsequent weighting acc. to mixCoeff.

object = "AcDcLcDistribution", fun = "ANY", cond = "ANY":

expectation by first coercing to class "UnivarLebDecDistribution" and using the corresponding method.

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

if we are in i.i.d. situation (i.e., slot SummandsDistr is of class UnivariateDistribution) the formula $E[N]E[S]$ for $N$ the frequency distribution and $S$ the summand distribution; else we coerce to "UnivarLebDecDistribution".

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

exact evaluation using explicit expressions.

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

for noncentrality 0 exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

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

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

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

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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

exact evaluation using explicit expressions.

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.

See Also

distrExIntegrate, m1df, m2df, Distribution-class

Examples

# mean of Exp(1) distribution
E <- Exp() 

E(E) ## uses explicit terms
E(as(E,"AbscontDistribution")) ## uses numerical integration
E(as(E,"UnivariateDistribution")) ## uses simulations
E(E, fun = function(x){2*x^2}) ## uses simulations

# the same operator for discrete distributions:
P <- Pois(lambda=2)

E(P) ## uses explicit terms
E(as(P,"DiscreteDistribution")) ## uses sums
E(as(P,"UnivariateDistribution")) ## uses simulations
E(P, fun = function(x){2*x^2}) ## uses simulations


# second moment of N(1,4)
E(Norm(mean=1, sd=2), fun = function(x){x^2})
E(Norm(mean=1, sd=2), fun = function(x){x^2}, useApply = FALSE)

# conditional distribution of a linear model
D1 <- LMCondDistribution(theta = 1) 
E(D1, cond = 1)
E(Norm(mean=1))
E(D1, function(x){x^2}, cond = 1)
E(Norm(mean=1), fun = function(x){x^2})
E(D1, function(x, cond){cond*x^2}, cond = 2, withCond = TRUE, useApply = FALSE)
E(Norm(mean=2), function(x){2*x^2})

E(as(Norm(mean=2),"AbscontDistribution"))
### somewhat less accurate:
E(as(Norm(mean=2),"AbscontDistribution"), 
     lowerTruncQuantil=1e-4,upperTruncQuantil=1e-4, IQR.fac= 4)
### even less accurate:
E(as(Norm(mean=2),"AbscontDistribution"), 
     lowerTruncQuantil=1e-2,upperTruncQuantil=1e-2, IQR.fac= 4)
### no good idea, but just as an example:
E(as(Norm(mean=2),"AbscontDistribution"), 
     lowerTruncQuantil=1e-2,upperTruncQuantil=1e-2, IQR.fac= .1)

### truncation of integration range; see also m1df...
E(Norm(mean=2), low=2,upp=4)

E(Cauchy())
E(Cauchy(),upp=3,low=-2)
# some Lebesgue decomposed distribution 
mymix <- UnivarLebDecDistribution(acPart = Norm(), discretePart = Binom(4,.4),
         acWeight = 0.4)
E(mymix)