expected.gld | R Documentation |
Returns the expected value of the Generalized Lambda Distribution
expected.gld(n=1, i=1, params) expected.gld.approx(n=1, i=1, params)
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 |
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
Robin K. S. Hankin
A. Ozturk and R. F. Dale, “Least squares estimation of the parameters of the generalized lambda distribution”, Technometrics 1985, 27(1):84 [it does not appear to be possible, as of R-2.9.1, to render the diacritic marks in the first author's names in a nicely portable way]
Gld
, expected.value
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.
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