lmomln3 {lmomco} | R Documentation |
This function estimates the L-moments of the Log-Normal3 distribution given the parameters
(xi, α, and kappa) from parln3
.
The L-moments in terms of the parameters are
λ_1 = xi + frac{α}{kappa}(1-e^{kappa^2/2}) mbox{ and}
λ_2 = frac{α}{kappa}(e^{kappa^2/2})(1-2Phi(-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.
lmomln3(para)
para |
The parameters of the distribution. |
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”. |
W.H. Asquith
NEED
lmr <- lmom.ub(c(123,34,4,654,37,78)) lmr lmomln3(parln3(lmr))