lmomco (version 0.88)

parpe3: Estimate the Parameters of the Pearson Type III Distribution

Description

This function estimates the parameters of the Pearson Type III distribution given the L-moments of the data in an L-moment object such as that returned by lmom.ub. The L-moments in terms of the parameters are complicated and solved numerically.

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

parpe3(lmom,checklmom=TRUE)

Arguments

lmom

A L-moment object created by lmom.ub or pwm2lmom.

checklmom

Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the $\tau_4$ and $\tau_3$ inequ

Value

• An R list is returned.
• type
  The type of distribution: pe3.
• para
  The parameters of the distribution.
• source
  The source of the parameters: parpe3.

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.

See Also

lmom.ub, lmompe3, cdfpe3, quape3

Examples

lmr <- lmom.ub(rnorm(20))
parpe3(lmr)