This function estimates the L-moments of the Rayleigh distribution given the parameters (\(\xi\) and \(\alpha\)) from parray. The L-moments in terms of the parameters are
$$\lambda_1 = \xi + \alpha\sqrt{\pi/2} \mbox{,}$$
$$\lambda_2 = \frac{1}{2} \alpha(\sqrt{2} - 1)\sqrt{\pi}\mbox{,}$$
$$\tau_3 = \frac{1 - 3/\sqrt{2} + 2/\sqrt{3}}{1 - 1/\sqrt{2}} = 0.1140 \mbox{, and}$$
$$\tau_4 = \frac{1 - 6/\sqrt{2} + 10/\sqrt{3} - 5\sqrt{4}}{1 - 1/\sqrt{2}} = 0.1054 \mbox{.}$$
Usage
lmomray(para)
Value
An R
list is returned.
lambdas
Vector of the L-moments. First element is
\(\lambda_1\), second element is \(\lambda_2\), and so on.
ratios
Vector of the L-moment ratios. Second element is
\(\tau\), third element is \(\tau_3\) and so on.
trim
Level of symmetrical trimming used in the computation, which is 0.
leftrim
Level of left-tail trimming used in the computation, which is NULL.
rightrim
Level of right-tail trimming used in the computation, which is NULL.
source
An attribute identifying the computational
source of the L-moments: “lmomray”.
Arguments
para
The parameters of the distribution.
Author
W.H. Asquith
References
Hosking, J.R.M., 1986, The theory of probability weighted moments: Research Report RC12210, IBM Research Division, Yorkton Heights, N.Y.