theoLmoms {lmomco} | R Documentation |
Compute the theoretrical L-moments for a vector. A theoretrical L-moment in integral form is
λ_r = frac{1}{r} sum^{r-1}_{k=0}{(-1)^k {r-1 choose k} frac{r!:I_r}{(r-k-1)!k!} } mbox{, in which }
I_r = int^1_0 X(F) times F^{r-k-1}(1-F)^{k},mathrm{d}F mbox{,}
where X(F) is the quantile function of the random variable X for nonexceedance probability F, and r represents the order of the L-moments. This function actually dispatches to theoTLmoms
with trim=0
argument.
theoLmoms(para,nmom=5,verbose=FALSE)
para |
A distribution parameter object of this package vec2par . |
nmom |
The number of moments to compute. Default is 5. |
verbose |
Toggle verbose output. Because the R function integrate is used to perform the numerical integration, it might be useful to see selected messages regarding the numerical integration. |
An R list
is returned.
lambdas |
Vector of the TL-moments. First element is λ_1, second element is λ_2, and so on. |
ratios |
Vector of the L-moment ratios. Second element is tau_2, third element is tau_3 and so on. |
trim |
Level of symmetrical trimming used in the computation, which will equal zero (the ordinary L-moments). |
source |
An attribute identifying the computational source of the L-moments: “theoTLmoms”. |
The actual function used is theoLmoms(para,nmom=nmom,trim=0,verbose=verbose
.
W.H. Asquith
Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.
theoTLmoms
, par2qua
, TLmoms
, lmom.ub
para <- vec2par(c(0,1),type='nor') # standard normal TL00 <- theoLmoms(para) # compute ordinary L-moments