This function estimates the parameters (\(\nu\) and \(\alpha\)) of the Rice distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between distribution parameters and L-moments are complex and tabular lookup is made using a relation between \(\tau\) and a form of signal-to-noise ratio \(\mathrm{SNR}\) defined as \(\nu/\alpha\) and a relation between \(\tau\) and precomputed Laguerre polynomial (LaguerreHalf).
The \(\lambda_1\) (mean) is most straightforward
$$
\lambda_1 = \alpha \times \sqrt{\pi/2} \times L_{1/2}(-\nu^2/[2\alpha^2])\mbox{,}
$$
for which the terms to the right of the multiplication symbol are uniquely a function of \(\tau\) and precomputed for tabular lookup and interpolation from sysdata.rdb (.lmomcohash$RiceTable). Parameter estimation also relies directly on tabular lookup and interpolation to convert \(\tau\) to \(\mathrm{SNR}\). The file SysDataBuilder.R provides additional technical details.
parrice(lmom, checklmom=TRUE, ...)An R
list is returned.
The type of distribution: rice.
The parameters of the distribution.
The source of the parameters: “parrice”.
A numeric failure mode.
A helpful message on the failure.
An L-moment object created by lmoms or vec2lmom.
Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the \(\tau_4\) and \(\tau_3\) inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check. However, the end point of the Rice distribution for high \(\nu/\alpha\) is not determined here, so it is recommended to leave checklmom turned on.
Other arguments to pass.
W.H. Asquith
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8.
lmomrice, cdfrice, pdfrice, quarice