# tlmrnor: Compute Select TL-moment ratios of the Normal Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function computes select TL-moment ratios of the Normal distribution for defaults of μ = 0 and σ = 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 μ and σ.

## Usage

 `1` ```tlmrnor(trim=NULL, leftrim=NULL, rightrim=NULL, mu=0, sigma=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. `mu` Location parameter (mean) of the distribution. `sigma` Scale parameter (standard deviation) 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

`quanor`, `theoTLmoms`
 ```1 2 3 4 5``` ```## Not run: tlmrnor(leftrim=2, rightrim=1) tlmrnor(leftrim=2, rightrim=1, mu=100, sigma=1000) # another slow example ## End(Not run) ```