theoLmoms: The Theoretical L-moments and L-moment Ratios using...

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

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

\lambda_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, minF=0, maxF=1)

Arguments

para	A distribution parameter object such as from 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.
minF	The end point of nonexceedance probability in which to perform the integration. Try setting to non-zero (but very small) if the integral is divergent.
maxF	The end point of nonexceedance probability in which to perform the integration. Try setting to non-unity (but still very close [perhaps 1 - minF]) if the integral is divergent.

Value

An R list is returned.

lambdas	Vector of the TL-moments. First element is \lambda_1, second element is \lambda_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 theoTLmoms(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, v. 52, pp. 105–124.

See Also

theoTLmoms

Examples

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

lmomco documentation built on Aug. 30, 2023, 5:10 p.m.