This document shows a comparison of computation time of TL-moments between different packages available, as well as between the different approaches built-in in this package.
This package offers the following computation methods (available via computation.method
-attribute in TLMoments
or TLMoment
):
direct
: Calculation as a weighted mean of the ordered data vector
pwm
: Calculation of probabilty-weighted moments and using the conversion to TL-moments
recursive
: An alternative recursive estimation of the weights of the direct approach
recurrence
: Estimating the L-moments first and using the recurrence property to derive TL-moments
For a complete and thorough analysis of all these approaches and another speed comparison see Hosking & Balakrishnan (2015, A uniqueness result for L-estimators, with applications to L-moments, Statistical Methodology, 24, 69-80).
Besides our implementation, L-moments and/or TL-moments can be calculated using the packages
lmomco
: L-moments and TL-moments
Lmoments
: L-moments and TL(1,1)-moments
lmom
: only L-moments
(all availabe at CRAN). The functions lmomco::lmoms
, lmomco::TLmoms
, and Lmoments::Lmoments
return list objects with (T)L-moments and (T)L-moment-ratios and are therefore compared to our TLMoments
; lmom::samlmu
returns a vector of lambdas and is compared to TLMoment
(which is a fast bare-bone function to compute TL-moments but is not suited to be transmitted to parameters
or other functions of this package).
First we check, if all approaches give the same results (lmomco::lmoms is added as comparison).
n <- c(25, 50, 100, 200, 500, 1000, 10000, 50000)
sapply(n, function(nn) {
x <- evd::rgev(nn)
check <- lmomco::lmoms(x, 4)$lambdas
sapply(c("direct", "pwm", "recursive"), function(comp) {
isTRUE(all.equal(TLMoment(x, order = 1:4, computation.method = comp), check, check.attributes = FALSE))
})
})
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## direct TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## pwm TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## recursive TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
Now we compare the functions giving L-moments are L-moment-ratios simultaneously.
possib <- list(
TLMoments_direct = function(x) TLMoments(x, max.order = 4, computation.method = "direct"),
TLMoments_pwm = function(x) TLMoments(x, max.order = 4, computation.method = "pwm"),
TLMoments_recursive = function(x) TLMoments(x, max.order = 4, computation.method = "recursive"),
lmomco = function(x) lmomco::lmoms(x, 4),
Lmoments = function(x) Lmoments::Lmoments(x, returnobject = TRUE)
)
# n = 50
datalist <- replicate(200, evd::rgev(50), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 0.043
## TLMoments_pwm 0.037
## TLMoments_recursive 0.033
## lmomco 0.634
## Lmoments 0.054
# n = 1000
datalist <- replicate(200, evd::rgev(1000), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 0.181
## TLMoments_pwm 0.123
## TLMoments_recursive 0.057
## lmomco 11.880
## Lmoments 0.120
As we see, our implementation of the recursive approach is clearly the fastest. After this, the pwm approach is to be prefered over the direct approach. The implementation in lmomco
is slow, compared to the others, especially for longer data vectors. Lmoments
is constantly slower than the recursive approach of this package.
Comparison of functions that only return a vector of L-moments:
possib <- list(
TLMoments_direct = function(x) TLMoment(x, order = 1:4, computation.method = "direct"),
TLMoments_pwm = function(x) TLMoment(x, order = 1:4, computation.method = "pwm"),
TLMoments_recursive = function(x) TLMoment(x, order = 1:4, computation.method = "recursive"),
lmom = function(x) lmom::samlmu(x, 4),
Lmoments = function(x) Lmoments::Lmoments(x, returnobject = FALSE)
)
# n = 50
datalist <- replicate(200, evd::rgev(50), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 0.011
## TLMoments_pwm 0.008
## TLMoments_recursive 0.005
## lmom 0.009
## Lmoments 0.048
# n = 1000
datalist <- replicate(200, evd::rgev(1000), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 0.137
## TLMoments_pwm 0.084
## TLMoments_recursive 0.023
## lmom 0.010
## Lmoments 0.087
For smaller data vectors our implementation is the fastest, but with longer data vectors lmom::samlmu
excels.
First we check, if all approaches give the same results (lmomco::Tlmoms is added as comparison)
n <- c(25, 50, 100, 150, 200, 500, 1000, 10000)
sapply(n, function(nn) {
x <- evd::rgev(nn)
check <- lmomco::TLmoms(x, 4, leftrim = 0, rightrim = 1)$lambdas
sapply(c("direct", "pwm", "recursive", "recurrence"), function(comp) {
isTRUE(all.equal(TLMoment(x, order = 1:4, rightrim = 1, computation.method = comp), check, check.attributes = FALSE))
})
})
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## direct TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## pwm TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## recursive TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE
## recurrence TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
sapply(n, function(nn) {
x <- evd::rgev(nn)
check <- lmomco::TLmoms(x, 4, leftrim = 2, rightrim = 4)$lambdas
sapply(c("direct", "pwm", "recursive", "recurrence"), function(comp) {
isTRUE(all.equal(TLMoment(x, order = 1:4, leftrim = 2, rightrim = 4, computation.method = comp), check, check.attributes = FALSE))
})
})
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## direct TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## pwm TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## recursive TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE
## recurrence TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
The recursive approach fails when n exceeds 150. All other implementations give the same results.
possib <- list(
TLMoments_direct = function(x) TLMoments(x, leftrim = 0, rightrim = 1, max.order = 4, computation.method = "direct"),
TLMoments_pwm = function(x) TLMoments(x, leftrim = 0, rightrim = 1, max.order = 4, computation.method = "pwm"),
TLMoments_recurrence = function(x) TLMoments(x, leftrim = 0, rightrim = 1, max.order = 4, computation.method = "recurrence"),
lmomco = function(x) lmomco::TLmoms(x, 4, leftrim = 0, rightrim = 1)
)
# n = 50
datalist <- replicate(200, evd::rgev(50), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 0.093
## TLMoments_pwm 0.041
## TLMoments_recurrence 0.036
## lmomco 0.632
# n = 1000
datalist <- replicate(200, evd::rgev(1000), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 1.273
## TLMoments_pwm 0.151
## TLMoments_recurrence 0.057
## lmomco 12.251
possib <- list(
TLMoments_direct = function(x) TLMoments(x, leftrim = 2, rightrim = 4, max.order = 4, computation.method = "direct"),
TLMoments_pwm = function(x) TLMoments(x, leftrim = 2, rightrim = 4, max.order = 4, computation.method = "pwm"),
TLMoments_recurrence = function(x) TLMoments(x, leftrim = 2, rightrim = 4, max.order = 4, computation.method = "recurrence"),
lmomco = function(x) lmomco::TLmoms(x, 4, leftrim = 2, rightrim = 4)
)
# n = 50
datalist <- replicate(200, evd::rgev(50), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 0.099
## TLMoments_pwm 0.047
## TLMoments_recurrence 0.038
## lmomco 0.590
# n = 1000
datalist <- replicate(200, evd::rgev(1000), simplify = FALSE)
do.call("rbind", lapply(possib, function(f) {
system.time(lapply(datalist, f))[3]
}))
## elapsed
## TLMoments_direct 1.292
## TLMoments_pwm 0.260
## TLMoments_recurrence 0.074
## lmomco 12.024
In this calculations the recurrence approach clearly outperforms the other implementations. Calculation using probabilty-weighted moments is relatively fast, but using the direct calculation should be avoided, regarding calculation speed. This package's implementation is clearly faster than those in lmomco
.
This results encourage to use the recursive approach for L-moments and the recurrence approach when calculating TL-moments. Therefore these are the defaults in this package, but the other computation methods (direct and pwm) are still available.