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distrEx (version 2.3.1)

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

Description

Generic function for the computation of (conditional) expectations.

Usage

E(object, fun, cond, ...)

## S3 method for class 'UnivariateDistribution,missing,missing':
E(object, 
             low = NULL, upp = NULL, Nsim = getdistrExOption("MCIterations"), ...)

## S3 method for class 'UnivariateDistribution,function,missing':
E(object, fun, 
        useApply = TRUE, low = NULL, upp = NULL,  Nsim = getdistrExOption("MCIterations"), ...)

## S3 method for class 'AbscontDistribution,function,missing':
E(object, fun, useApply = TRUE,
             low = NULL, upp = NULL, 
             rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ...)

## S3 method for class 'UnivarMixingDistribution,missing,missing':
E(object, low = NULL, 
             upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ...)

## S3 method for class 'UnivarMixingDistribution,function,missing':
E(object, fun, useApply = TRUE, 
             low = NULL, upp = NULL, 
             rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ...)

## S3 method for class 'UnivarMixingDistribution,missing,ANY':
E(object, cond, low = NULL, 
             upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ...)

## S3 method for class 'UnivarMixingDistribution,function,ANY':
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"), ...)

## S3 method for class 'DiscreteDistribution,function,missing':
E(object, fun, useApply = TRUE, 
             low = NULL, upp = NULL, ...)

## S3 method for class 'AffLinDistribution,missing,missing':
E(object, low = NULL, upp = NULL, ...)

## S3 method for class 'AffLinUnivarLebDecDistribution,missing,missing':
E(object, low = NULL, upp = NULL, ...)

## S3 method for class 'MultivariateDistribution,missing,missing':
E(object, 
             Nsim = getdistrExOption("MCIterations"), ...)
## S3 method for class 'MultivariateDistribution,function,missing':
E(object, fun, useApply = TRUE, 
             Nsim = getdistrExOption("MCIterations"), ...)

## S3 method for class 'DiscreteMVDistribution,missing,missing':
E(object, low = NULL, upp = NULL, ...)

## S3 method for class 'DiscreteMVDistribution,function,missing':
E(object, fun, 
             useApply = TRUE, ...)

## S3 method for class 'AbscontCondDistribution,missing,numeric':
E(object, cond, useApply = TRUE,
             low = NULL, upp = NULL, 
             rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ...)

## S3 method for class 'DiscreteCondDistribution,missing,numeric':
E(object, cond, useApply = TRUE,
             low = NULL, upp = NULL, ...)

## S3 method for class 'UnivariateCondDistribution,function,numeric':
E(object, fun, cond, 
              withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL,
              Nsim = getdistrExOption("MCIterations"), ...)

## S3 method for class 'AbscontCondDistribution,function,numeric':
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")
             , ...)

## S3 method for class 'DiscreteCondDistribution,function,numeric':
E(object, fun, cond, 
             withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL,...)

## S3 method for class 'DiscreteCondDistribution,function,numeric':
E(object, fun, cond, 
             withCond = FALSE, useApply = TRUE, low = NULL, upp = NULL,...)
             
## S3 method for class 'UnivarLebDecDistribution,missing,missing':
E(object, low = NULL, upp = NULL,  
             rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ... )
## S3 method for class 'UnivarLebDecDistribution,function,missing':
E(object, fun, 
             useApply = TRUE, low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ... )
## S3 method for class 'UnivarLebDecDistribution,missing,ANY':
E(object, cond, 
             low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ... )
## S3 method for class 'UnivarLebDecDistribution,function,ANY':
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"), ... )

## S3 method for class 'AcDcLcDistribution,ANY,ANY':
E(object, fun, cond, 
             low = NULL, upp = NULL, rel.tol= getdistrExOption("ErelativeTolerance"), 
             lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"), 
             upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
             IQR.fac = getdistrExOption("IQR.fac"), ... )
## S3 method for class 'CompoundDistribution,missing,missing':
E(object, low = NULL, upp = NULL, ...)

## S3 method for class 'Arcsine,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Beta,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Binom,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Cauchy,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Chisq,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Dirac,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'DExp,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Exp,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Fd,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Gammad,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Gammad,function,missing':
E(object, fun, low = NULL, upp = NULL, 
                                      rel.tol = getdistrExOption("ErelativeTolerance"),
                                      lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),
                                      upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
                                      IQR.fac = getdistrExOption("IQR.fac"), ...)
## S3 method for class 'Geom,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Gumbel,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'GPareto,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'GPareto,function,missing':
E(object, fun, low = NULL, upp = NULL, 
                                      rel.tol = getdistrExOption("ErelativeTolerance"),
                                      lowerTruncQuantile = getdistrExOption("ElowerTruncQuantile"),
                                      upperTruncQuantile = getdistrExOption("EupperTruncQuantile"), 
                                      IQR.fac = max(10000, getdistrExOption("IQR.fac")), ...)
## S3 method for class 'Hyper,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Logis,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Lnorm,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Nbinom,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Norm,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Pareto,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Pois,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Unif,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Td,missing,missing':
E(object, low = NULL, upp = NULL, ...)
## S3 method for class 'Weibull,missing,missing':
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 $\pm$IQR.fac$\times$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.

concept

  • expectation
  • conditional expectation
  • integration
  • functional
  • moment

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

Run this code
# 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)

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