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 $\gamma$) of the distribution computed by parpe3. The quantile function of the distribution 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, these 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 of the pmoms function documentation.

Usage

quape3(f, para, paracheck=TRUE)

Arguments

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

para

The parameters from parpe3 or similar.

paracheck

A logical controlling whether the parameters and 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 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, vol. 52, p. 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.

Examples

Run this code

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