theoLmoms {lmomco}R Documentation

The Theoretical L-moments and L-moment Ratios using Integration of the Quantile Function

Description

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.

Usage

theoLmoms(para,nmom=5,verbose=FALSE)

Arguments

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.

Value

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”.

Note

The actual function used is theoLmoms(para,nmom=nmom,trim=0,verbose=verbose.

Author(s)

W.H. Asquith

References

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.

See Also

theoTLmoms, par2qua, TLmoms, lmom.ub

Examples

para <- vec2par(c(0,1),type='nor') # standard normal
TL00 <- theoLmoms(para) # compute ordinary L-moments

[Package lmomco version 0.96.3 Index]