lmomco (version 1.4.3)

lmomln3: L-moments of the 3-Parameter Log-Normal Distribution

Description

This function estimates the L-moments of the Log-Normal3 distribution given the parameters ($\xi$, $\alpha$, and $\kappa$) from parln3. 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

lmomln3(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: lmomln3.

References

NEED

See Also

parln3, qualn3, cdfln3

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
lmr
lmomln3(parln3(lmr))