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)

Arguments

nowarning

Logical. Suppress a warning? Ignored for VGAM 0.9-7 and higher.

lvee, lsigma

Link functions for the \(v\) and \(\sigma\) parameters. See Links for more choices and for general information.

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 CommonVGAMffArguments for more information.

nsimEIM, zero

See CommonVGAMffArguments for information.

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.

Value

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

References

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

Author

T. W. Yee

Note

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 \(\sigma\).

See also

drice, rayleigh, besselI, simulate.vlm.

Examples

if (FALSE)  sigma <- exp(1); vee <- exp(2)
rdata <- data.frame(y = rrice(n <- 1000, sigma, vee = vee))
#> Error in rnorm(n, mean = vee * cos(theta), sd = sigma): invalid arguments
fit <- vglm(y ~ 1, riceff, data = rdata, trace = TRUE, crit = "c")
#> Error in eval(mf, parent.frame()): object 'rdata' not found
c(with(rdata, mean(y)), fitted(fit)[1])
#> Error: object 'rdata' not found
coef(fit, matrix = TRUE)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'coef': object 'fit' not found
Coef(fit)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'Coef': object 'fit' not found
summary(fit)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'fit' not found
 # \dontrun{}