lmomco (version 0.88)

lmomcau: Trimmed L-moments of the Cauchy Distribution

Description

This function estimates the trimmed L-moments of the Cauchy distribution given the parameters ($\xi$ and $\alpha$) from parcau. The trimmed L-moments in terms of the parameters are

$$\lambda^{(1)}_1 = \xi \mbox{,}$$ $$\lambda^{(1)}_2 = 0.698\alpha \mbox{,}$$ $$\tau^{(1)}_3 = 0 \mbox{, and}$$ $$\tau^{(1)}_4 = 0.343 \mbox{.}$$

Usage

lmomcau(para)

Arguments

para

The parameters of the distribution.

Value

• An R list is returned.
• lambdas
  Vector of the trimmed L-moments. First element is $\lambda^{(1)}_1$, second element is $\lambda^{(1)}_2$, and so on.
• ratios
  Vector of the L-moment ratios. Second element is $\tau^{(1)}$, third element is $\tau^{(1)}_3$ and so on.
• source
  An attribute identifying the computational source of the L-moments: lmomcau
• trim
  Level of symmetrical trimming used---trim=1.

References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299--314.

Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.

See Also

parcau, quacau, cdfcau

Examples

X1 <- rcauchy(20)
lmomcau(parcau(TLmoms(X1,trim=1)))