riceff {VGAM} | R Documentation |
Estimates the two parameters of a Rice distribution by maximum likelihood estimation.
riceff(lvee="loge", lsigma="loge", evee=list(), esigma=list(), ivee=NULL, isigma=NULL, nsimEIM=100, zero=NULL)
lvee, evee |
Link function and extra argument for the v parameter.
See Links for more choices and for general information.
|
lsigma, esigma |
Link function and extra argument for the sigma parameter.
See Links for more choices and for general information.
|
ivee, isigma |
Optional initial values for the parameters.
See CommonVGAMffArguments for more information.
If convergence failure occurs (this VGAM family function seems
to require good initial values) try using these arguments.
|
nsimEIM, zero |
See CommonVGAMffArguments for more information.
|
The Rice distribution has density function
f(y;v,sigma) = (y/sigma^2) * exp(-(y^2+v^2) / (2*sigma^2)) * I_0(y*v/sigma^2)
where y>0, v > 0, σ > 0 and I_0 is the modified Bessel function of the first kind with order zero. When v=0 the Rice distribution reduces to a Rayleigh distribution. The mean is sigma*sqrt(pi/2)*exp(z/2)*((1-z)*I_0(-z/2)-z*I_1(-z/2)) (returned as the fitted values) where z=-v^2/(2*sigma^2). Simulated Fisher scoring is implemented.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
and vgam
.
Convergence problems may occur for data where v=0; if so, use
rayleigh
or possibly use an identity
link.
When v is large (greater than 3, say) then the mean is approximately v and the standard deviation is approximately sigma.
T. W. Yee
Rice, S. O. (1945) Mathematical Analysis of Random Noise. Bell System Technical Journal, 24, 46–156.
vee = exp(2); sigma = exp(1); y = rrice(n <- 1000, vee, sigma) fit = vglm(y ~ 1, riceff, trace=TRUE, crit="c") c(mean(y), fitted(fit)[1]) coef(fit, matrix=TRUE) Coef(fit) summary(fit)