lmomco (version 2.4.14)

tlmr2par: Sample Trimmed L-moments to Fitted Distribution

Description

Parameter estimation of a distribution given initial estimate of the parameters of the distribution to the sample trimmed L-moment (TL-moment) using numerical optimization. Thought the TL-moments can be used with substantial depth into either tail and need not be symmetrically trimmed, the TL-moments do not appear as useful when substantial tail trimming is needed, say for mix population mitigation. Then censored or truncation methods might be preferred. The x2xlo family of operations can be used for conditional left-tail truncation, which is not uncommon in frequency analyses of rail-tail interest water resources phenomena.

Usage

tlmr2par(x, type, init.para=NULL, trim=NULL, leftrim=NULL, rightrim=NULL, ...)

Value

An R

list is returned. This list should contain at least the following items, but some distributions such as the revgum have extra.

type

The type of distribution in three character (minimum) format.

para

The parameters of the distribution.

text

Optional material. If the solution fails but the optimization appears to converge, then this element is inserted into the list and the para will be all NA.

source

Attribute specifying source of the parameters.

rt

The list from the optim() function.

init.para

A copy of the initial parameters given.

Arguments

x

A vector of data values.

type

Three character (minimum) distribution type (for example, type="gev", see dist.list.

init.para

Initial parameters as a vector \(\Theta\) or as an lmomco parameter “object” from say vec2par. If a vector is given, then internally vec2par is called with distribution equal to type.

trim

Level of symmetrical trimming to use in the computations. Although NULL is in the argument list, the default is 0---the usual L-moment is returned.

leftrim

Level of trimming of the left-tail of the sample, which should be left to NULL if no or symmetrical trimming is used.

rightrim

Level of trimming of the right-tail of the sample, which should be left to NULL if no or symmetrical trimming is used.

...

Other arguments to pass to the optim() function.

Author

W.H. Asquith

References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, v. 43, pp. 299--314.

See Also

theoTLmoms, TLmoms, lmr2par

Examples

# \donttest{
# (1) An example to check that trim(0,0) should recover whole sample
the.data <- rlmomco(140, vec2par(c(3, 0.4, -0.1), type="pe3"))
wild.guess <- vec2par(c(mean(the.data), 1, 0),    type="pe3")
pe3whole <- lmom2par(lmoms(the.data),             type="pe3")
pe3trimA  <- tlmr2par(the.data, "pe3", init.para=wild.guess, leftrim=0,  rightrim=0)
pe3trimB  <- tlmr2par(the.data, "pe3", init.para=wild.guess, leftrim=10, rightrim=3)
message("PE3 parent       = ", paste0(pe3whole$para, sep=" "))
message("PE3 whole sample = ", paste0(pe3whole$para, sep=" "))
message("PE3 trim( 0, 0)  = ", paste0(pe3trimA$para, sep=" "))
message("PE3 trim(10, 3)  = ", paste0(pe3trimB$para, sep=" ")) ## }

# \donttest{
# (2) An example with "real" outliers
FF <- lmomco::nonexceeds(); qFF <- qnorm(FF); type <- "gev"
the.data <- c(3.064458, 3.139879, 3.167317, 3.225309, 3.324282, 3.330414,
             3.3304140, 3.340444, 3.357935, 3.376577, 3.378398, 3.392697,
             3.4149730, 3.421604, 3.424882, 3.434569, 3.448706, 3.451786,
             3.4517860, 3.462398, 3.465383, 3.469822, 3.491362, 3.501059,
             3.5224440, 3.523746, 3.527630, 3.527630, 3.531479, 3.546543,
             3.5932860, 3.597695, 3.600973, 3.614897, 3.620136, 3.660865,
             3.6848450, 3.820858, 4.708421)
the.data <- sort(the.data) # though already sorted, backup for plotting needs

# visually, looks like 4 outliers to the left and one outlier to the right
# perhaps the practical situation is that we do not wan the left tail to
# mess up the right when fitting a distribution because maybe the practical
# aspects are the that right tail is of engineering interest, but then we
# have some idea that the one very large event is of questionable suitability
t1 <- 4; t2 <- 1 # see left and right trimming and then estimation parameters
whole.para <- lmom2par(lmoms(the.data), type=type)
trim.para  <- tlmr2par(the.data, type, init.para=whole.para, leftrim=t1, rightrim=t2)

n <- length(the.data)
cols <- rep(grey(0.5), n)
pchs <- rep(1, n)
if(t1 != 0) {
  cols[      1 :t1] <- "red"
  cols[(n-t2+1):n ] <- "purple"
}
if(t2 != 0) {
  pchs[      1 :t1] <- 16
  pchs[(n-t2+1):n ] <- 16
}
plot( qFF, qlmomco(FF, whole.para), type="l", lwd=2, ylim=c(3.1,4.8),
           xlab="Standard normal variate",
           ylab="Some phenomena, log10(cfs)")
lines(qFF, qlmomco(FF, trim.para), col=4, lwd=3)
points(qnorm(pp(the.data)), sort(the.data), pch=pchs, col=cols)
legend("topleft", c("L-moments",
                   paste0("TL-moments(", t1, ",", t2,")")), bty="n",
                  lty=c(1,1), lwd=c(2,3), col=c(1,4))
# see the massive change from the whole sample to the trim(t1,t2) curve# }