lmomco (version 1.4.3)

tlmrgum: Compute Select TL-moment ratios of the Gumbel Distribution

Description

This function computes select TL-moment ratios of the Gumbel 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 a dependent on the values for $\xi$ and $\alpha$.

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

Usage

tlmrgum(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.

See Also

quagum, theoTLmoms

Examples

tlmrgum(trim=2)
tlmrgum(trim=2, xi=2)