lmomco (version 0.88)

lmompe3: L-moments of the Pearson Type III Distribution

Description

This function estimates the L-moments of the Pearson Type III distribution given the parameters ($\mu$, $\sigma$, and $\gamma$) from parpe3. 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

lmompe3(para)

Arguments

para

The parameters of the distribution.

Value

• An R list is returned.
• L1
  Arithmetic mean.
• L2
  L-scale---analogous to standard deviation.
• LCV
  coefficient of L-variation---analogous to coe. of variation.
• TAU3
  The third L-moment ratio or L-skew---analogous to skew.
• TAU4
  The fourth L-moment ratio or L-kurtosis---analogous to kurtosis.
• TAU5
  The fifth L-moment ratio.
• L3
  The third L-moment.
• L4
  The fourth L-moment.
• L5
  The fifth L-moment.
• source
  An attribute identifying the computational source of the L-moments: lmompe3.

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

parpe3, quape3, cdfpe3

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
lmr
lmompe3(parpe3(lmr))