tlmrcau: Compute Select TL-moment ratios of the Cauchy Distribution

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

Compute Select TL-moment ratios of the Cauchy Distribution

Description

This function computes select TL-moment ratios of the Cauchy distribution for defaults of \xi = 0 and \alpha = 1. This function can be useful for plotting the trajectory of the distribution on TL-moment ratio diagrams of \tau^{(t_1,t_2)}_2, \tau^{(t_1,t_2)}_3, \tau^{(t_1,t_2)}_4, \tau^{(t_1,t_2)}_5, and \tau^{(t_1,t_2)}_6. In reality, \tau^{(t_1,t_2)}_2 is dependent on the values for \xi and \alpha.

Usage

tlmrcau(trim=NULL, leftrim=NULL, rightrim=NULL, xi=0, alpha=1)

Arguments

trim	Level of symmetrical trimming to use in the computations. Although NULL in the argument list, the default is 0—the usual L-moment ratios are returned.
leftrim	Level of trimming of the left-tail of the sample.
rightrim	Level of trimming of the right-tail of the sample.
xi	Location parameter of the distribution.
alpha	Scale parameter of the distribution.

Value

An R list is returned.

tau2	A vector of the \tau^{(t_1,t_2)}_2 values.
tau3	A vector of the \tau^{(t_1,t_2)}_3 values.
tau4	A vector of the \tau^{(t_1,t_2)}_4 values.
tau5	A vector of the \tau^{(t_1,t_2)}_5 values.
tau6	A vector of the \tau^{(t_1,t_2)}_6 values.

Note

The function uses numerical integration of the quantile function of the distribution through the theoTLmoms function.

Author(s)

W.H. Asquith

See Also

quacau, theoTLmoms

Examples

## Not run: 
tlmrcau(trim=2)
tlmrcau(trim=2, xi=2) # another slow example

## End(Not run)

lmomco documentation built on May 29, 2024, 10:06 a.m.