# riceUC: The Rice Distribution

Description Usage Arguments Details Value Author(s) See Also Examples

### Description

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

### Usage

 ```1 2 3 4``` ```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) ```

### 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.

### 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.

### Value

`drice` gives the density, `price` gives the distribution function, `qrice` gives the quantile function, and `rrice` generates random deviates.

### Author(s)

T. W. Yee and Kai Huang

`riceff`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```## 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) ```

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