lmomco (version 0.6)

parcau: Estimate the Parameters of the Cauchy Distribution

Description

This function estimates the parameters of the Cauchy distribution from the trimmed L-moments (TL-moments) having trim level 1.

Usage

parcau(lmom)

Arguments

lmom

TL-moments from TLmoms with trim=1.

Value

• An R list is returned.
• type
  The type of distribution: cau.
• para
  The parameters of the distribution.

Details

Unlike many of the other distributions in this package, the parameter estimation occurs by passing the data into the function and not from passing of an L-moment object (see lmom.ub). Contrast this practice with pargum for example.) The reason this is so is because the usual L-moments are undefined for the Cauchy distribution, but the trimmed L-moments with a symmetrical trimming parameter are defined. Specifically, the L-moments by trimming the smallest and largest order statistic expections of the Cauchy are defined by Elamir and Seheult (2003). The function parcau calls TLlmoms(x,trim=1)) internally to compute the trimmed L-moments. The relation between the parameters and the trimmed L-moments is

$$\xi = \lambda^{(1)}_1 \mbox{and}$$

$$\alpha = \frac{\lambda^{(1)}_2}{0.698} \mbox{.}$$

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

TLmoms, lmomcau

Examples

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