lmomco (version 2.4.14)

quawak: Quantile Function of the Wakeby Distribution

Description

This function computes the quantiles of the Wakeby distribution given parameters (\(\xi\), \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\)) computed by parwak. The quantile function is $$x(F) = \xi+\frac{\alpha}{\beta}(1-(1-F)^\beta)- \frac{\gamma}{\delta}(1-(1-F))^{-\delta} \mbox{,}$$ where \(x(F)\) is the quantile for nonexceedance probability \(F\), \(\xi\) is a location parameter, \(\alpha\) and \(\beta\) are scale parameters, and \(\gamma\) and \(\delta\) are shape parameters. The five returned parameters from parwak in order are \(\xi\), \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\).

Usage

quawak(f, wakpara, paracheck=TRUE)

Value

Quantile value for nonexceedance probability \(F\).

Arguments

f

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

wakpara

The parameters from parwak 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 quantile function in the context of TL-moments with nonzero trimming.

Author

W.H. Asquith

References

Hosking, J.R.M., 1990, L-moments---Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, v. 52, pp. 105--124.

Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

See Also

cdfwak, pdfwak, lmomwak, parwak

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  quawak(0.5,parwak(lmr))