VGAM (version 0.8-3)

riceff: Rice Distribution Family Function

Description

Estimates the two parameters of a Rice distribution by maximum likelihood estimation.

Usage

riceff(lvee="loge", lsigma="loge", evee=list(), esigma=list(),
       ivee=NULL, isigma=NULL, nsimEIM=100, zero=NULL)

Arguments

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 init

nsimEIM, zero

See CommonVGAMffArguments for more information.

Value

• An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Details

The Rician distribution has density function $$f(y;v,\sigma) = \frac{ y }{\sigma^2} \, \exp(-(y^2+v^2) / (2\sigma^2)) \, I_0(y v / \sigma^2)$$ where $y > 0$, $v > 0$, $\sigma > 0$ 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.

References

Rice, S. O. (1945) Mathematical Analysis of Random Noise. Bell System Technical Journal, 24, 46--156.

See Also

drice, rayleigh, besselI.

Examples

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)