quacau {lmomco}

Quantile Function of the Cauchy Distribution

Description

This function computes the quantiles of the Cauchy distribution given parameters (\xi and \alpha) of the distribution provided by parcau. The quantile function of the distribution is

x(F) = \xi + \alpha \times \tan\bigl(\pi(F-0.5)\bigr) \mbox{,}

where x(F) is the quantile for nonexceedance probability F, \xi is a location parameter and \alpha is a scale parameter. The quantile function of the Cauchy distribution is supported by R function qcauchy. This function does not use qcauchy because qcauchy does not return Inf for F = 1 although it returns -Inf for F = 0.

Usage

quacau(f, para, paracheck=TRUE)

Arguments

f

Nonexceedance probability (0 \le F \le 1).

para

The parameters from parcau or vec2par.

paracheck

A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the distribution quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for for nonexceedance probability F.

Author(s)

W.H. Asquith

References

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

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

See Also

cdfcau, pdfcau, lmomcau, parcau

Examples

  para <- c(12,12)
  quacau(.5,vec2par(para,type='cau'))