Rice Distribution Family Function
Estimates the two parameters of a Rice distribution by maximum likelihood estimation.
riceff(lsigma = "loglink", lvee = "loglink", isigma = NULL,
ivee = NULL, nsimEIM = 100, zero = NULL, nowarning = FALSE)nowarning |
Logical. Suppress a warning? Ignored for VGAM 0.9-7 and higher. |
lvee, lsigma |
Link functions for the v and sigma parameters.
See |
ivee, isigma |
Optional initial values for the parameters.
If convergence failure occurs (this VGAM family function seems
to require good initial values) try using these arguments.
See |
nsimEIM, zero |
See |
The Rician 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.
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.
## Not run: sigma <- exp(1); vee <- exp(2) rdata <- data.frame(y = rrice(n <- 1000, sigma, vee = vee)) fit <- vglm(y ~ 1, riceff, data = rdata, trace = TRUE, crit = "coef") c(with(rdata, mean(y)), fitted(fit)[1]) coef(fit, matrix = TRUE) Coef(fit) summary(fit) ## End(Not run)
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