lmomco (version 2.2.5)

quape3: Quantile Function of the Pearson Type III Distribution

Description

This function computes the quantiles of the Pearson Type III distribution given parameters ($\mu$, $\sigma$, and $\gamma$) computed by parpe3. The quantile function has no explicit form (see cdfpe3).

For the implementation in the lmomco package, the three parameters are $\mu$, $\sigma$, and $\gamma$ for the mean, standard deviation, and skew, respectively. Therefore, the Pearson Type III distribution is of considerable theoretical interest to this package because the parameters, which are estimated via the L-moments, are in fact the product moments, although, the values fitted by the method of L-moments will not be numerically equal to the sample product moments. Further details are provided in the Examples section under pmoms.

Usage

quape3(f, para, paracheck=TRUE)

Arguments

f

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

para

The parameters from parpe3 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.

Value

Quantile value for nonexceedance probability $F$.

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

cdfpe3, pdfpe3, lmompe3, parpe3

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  quape3(0.5,parpe3(lmr))