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)

Arguments

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

para

The parameters from parpe3 or similar.

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))