VGAM (version 1.1-9)

Rice: The Rice Distribution

Description

Density, distribution function, quantile function and random generation for the Rician distribution.

Usage

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)

Value

drice gives the density,

price gives the distribution function,

qrice gives the quantile function, and

rrice generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

number of observations. Same as in runif.

vee, sigma

See riceff.

...

Other arguments such as lower.tail.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Author

T. W. Yee and Kai Huang

Details

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.

See Also

riceff.

Examples

if (FALSE)  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 v values")
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",
     main = "Blue is density, orange is CDF", col = "blue",
     ylim = c(0, 1), sub = "Red 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 = "red", lty = 3, type = "h")
lines(x, price(x, sigma, vee = vee), type = "l", col = "orange")
lines(Q, drice(Q, sigma, vee = vee), col = "red", lty = 3, type = "h")
lines(Q, price(Q, sigma, vee = vee), col = "red", lty = 3, type = "h")
abline(h = probs, col = "red", lty = 3)
max(abs(price(Q, sigma, vee = vee) - probs))  # Should be 0