The Rice Distribution
Density, distribution function, quantile function and random generation for the Rician distribution.
drice(x, sigma, vee, log = FALSE) price(q, sigma, vee, lower.tail = TRUE, log.p = FALSE, ...) qrice(p, sigma, vee, lower.tail = TRUE, log.p = FALSE, ...) rrice(n, sigma, vee)
See riceff, the VGAM family function
for estimating the two parameters,
for the formula of the probability density function and other details.
Formulas for price() and qrice() are based on the
Marcum-Q function.
drice gives the density,
price gives the distribution function,
qrice gives the quantile function, and
rrice generates random deviates.
T. W. Yee and Kai Huang
## Not run: x <- seq(0.01, 7, len = 201)
plot(x, drice(x, vee = 0, sigma = 1), type = "n", las = 1,, ylab = "",
main = "Density of Rice distribution for various values of v")
sigma <- 1; vee <- c(0, 0.5, 1, 2, 4)
for (ii in 1:length(vee))
lines(x, drice(x, vee = vee[ii], sigma), col = ii)
legend(x = 5, y = 0.6, legend = as.character(vee),
col = 1:length(vee), lty = 1)
x <- seq(0, 4, by = 0.01); vee <- 1; sigma <- 1
probs <- seq(0.05, 0.95, by = 0.05)
plot(x, drice(x, vee = vee, sigma = sigma), type = "l", col = "blue",
main = "Blue is density, orange is cumulative distribution function",
ylim = c(0, 1), sub = "Purple are 5, 10, ..., 95 percentiles",
las = 1, ylab = "", cex.main = 0.9)
abline(h = 0:1, col = "black", lty = 2)
Q <- qrice(probs, sigma, vee = vee)
lines(Q, drice(qrice(probs, sigma, vee = vee),
sigma, vee = vee), col = "purple", lty = 3, type = "h")
lines(x, price(x, sigma, vee = vee), type = "l", col = "orange")
lines(Q, drice(Q, sigma, vee = vee), col = "purple", lty = 3, type = "h")
lines(Q, price(Q, sigma, vee = vee), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(price(Q, sigma, vee = vee) - probs)) # Should be 0
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.