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.
quape3(f, para, paracheck=TRUE)Nonexceedance probability (\(0 \le F \le 1\)).
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.
Quantile value for nonexceedance probability \(F\).
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.
# NOT RUN {
lmr <- lmoms(c(123,34,4,654,37,78))
quape3(0.5,parpe3(lmr))
# }
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