lmomco (version 0.88)

lmomgno: L-moments of the Generalized Normal Distribution

Description

This function estimates the L-moments of the Generalized Normal (log-Normal) distribution given the parameters ($\xi$, $\alpha$, and $\kappa$) from pargno. The L-moments in terms of the parameters are

$$\lambda_1 = \xi + \frac{\alpha}{\kappa}(1-e^{\kappa^2/2}) \mbox{ and}$$ $$\lambda_2 = \frac{\alpha}{\kappa}(e^{\kappa^2/2})(1-2\Phi(-\kappa/\sqrt{2})) \mbox{,}$$

where $\Phi$ is the cumulative distribution of the standard normal distribution. There are no simple expressions for $\tau_3$, $\tau_4$, and $\tau_5$. Log transformation of the data prior to fitting of the Generalized Normal distribution is not required.

Usage

lmomgno(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: lmomgno.

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

pargno, quagno, cdfgno

Examples

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