lmomco (version 0.88)

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.
• source
  The source of the parameters: parcau.

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))