expected.gld {Davies}R Documentation

expected value of the Generalized Lambda Distribution

Description

Returns the expected value of the Generalized Lambda Distribution

Usage

expected.gld(n=1, i=1, params)
expected.gld.approx(n=1, i=1, params)

Arguments

n Number of observations
i Order statistic: i=1 means the smallest of n, and n=i means the largest
params The four parameters of a GLD distribution

Details

expected.gld and expected.approx return the exact and approximate values of the expected value of a Generalized Lambda Distribution RV.

Exploits the fact that the gld quantile function is the sum of a constant and two davies quantile functions.

Author(s)

Robin K. S. Hankin

References

A. "{O}zt"{u}rk and R. F. Dale, "Least squares estimation of the parameters of the generalized lambda distribution", Technometrics 1985, 27(1):84

See Also

Gld , expected.value

Examples

params <- c(4.114,0.1333,0.0193,0.1588)
mean(rgld(1000,params))
expected.gld(n=1,i=1,params)
expected.gld.approx(n=1,i=1,params)

f <- function(n){apply(matrix(rgld(n+n,params),2,n),2,min)}
#ie f(n) gives the smaller of 2 rgld RVs, n times.

mean(f(1000))
expected.gld(n=2,i=1,params)
expected.gld.approx(n=2,i=1,params)

plot(1:100,expected.gld.approx(n=100,i=1:100,params)-expected.gld(n=100,i=1:100,params))
# not bad, eh? ....yyyeeeeesss, but the parameters given by Ozturk give
#an almost zero second derivative for d(qgld)/dp, so the good agreement
#isn't surprising really.  Observe that the error is minimized at about
#p=0.2, where the point of inflection is.


[Package Davies version 0.1-4 Index]