theoLmoms {lmomco}

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, minF=0, maxF=1, quafunc=NULL,
                nsim=50000, fold=5,
                silent=TRUE, verbose=FALSE, ...)

Arguments

para

A distribution parameter object such as from vec2par.

nmom

The number of moments to compute. Default is 5.

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.

quafunc

An optional and arbitrary quantile function that simply needs to except a nonexceedance probability and the parameter object in para. This is a feature that permits computation of the L-moments of a quantile function that does not have to be implemented in the greater overhead hassles of the lmomco style. This feature might be useful for estimation of quantile function mixtures or those distributions not otherwise implemented in this package.

nsim

Simulation size for Monte Carlo integration is such is internally deemed necessary (see silent argument).

fold

The number of fractions or number of folds of nsim, which in other words, means that nsim is divided by folds and a loop creating folds integrations of nsim/folds is used from which the mean and mean absolute error of the integrand are computed. This is to try to recover similar output as integrate().

silent

The argument of silent for the try() operation wrapped on integrate(). If set true and the integral is probability divergent, Monte Carlo integration is triggered using nsim and folds. The user would have to set verbose=TRUE to then acquire the returned table in integration_table of the integration passes including those are or are not Monte Carlo.

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.

...

Additional arguments to pass.

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) because this function dispatches to theoTLmoms.

source

An attribute identifying the computational source of the L-moments: “theoLmoms”.

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