Compute Select TL-moment ratios of the Cauchy Distribution

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Description

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

Usage

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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 τ^{(t_1,t_2)}_2 values.

tau3

A vector of the τ^{(t_1,t_2)}_3 values.

tau4

A vector of the τ^{(t_1,t_2)}_4 values.

tau5

A vector of the τ^{(t_1,t_2)}_5 values.

tau6

A vector of the τ^{(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

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

## End(Not run)

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