quacau {lmomco}R Documentation

Quantile Function of the Cauchy Distribution

Description

This function computes the quantiles of the Cauchy distribution given parameters (xi and α) of the distribution provided by vec2par. The quantile function of the distribution is

x(F) = xi + α times tan(π(F-0.5)) mbox{,}

where x(F) is the quantile for nonexceedance probability F, xi is a location parameter and α is a scale parameter. R supports the quantile function of the Cauchy distribution through 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)

Arguments

f Nonexceedance probability (0 <= F <= 1).
para The parameters from parcau or vec2par.

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, vol. 43, pp. 299–314.

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

See Also

cdfcau, parcau, vec2par

Examples

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

[Package lmomco version 0.96.3 Index]