# nakagamiUC: Nakagami Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

Density, cumulative distribution function, quantile function and random generation for the Nakagami distribution.

## Usage

 ```1 2 3 4``` ```dnaka(x, scale = 1, shape, log = FALSE) pnaka(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) qnaka(p, scale = 1, shape, ...) rnaka(n, scale = 1, shape, Smallno = 1.0e-6) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. Same as in `runif`. `scale, shape` arguments for the parameters of the distribution. See `nakagami` for more details. For `rnaka`, arguments `shape` and `scale` must be of length 1. `Smallno` Numeric, a small value used by the rejection method for determining the upper limit of the distribution. That is, `pnaka(U) > 1-Smallno` where `U` is the upper limit. `...` Arguments that can be passed into `uniroot`. `log` Logical. If `log = TRUE` then the logarithm of the density is returned. `lower.tail, log.p` Same meaning as in `pnorm` or `qnorm`.

## Details

See `nakagami` for more details.

## Value

`dnaka` gives the density, `pnaka` gives the cumulative distribution function, `qnaka` gives the quantile function, and `rnaka` generates random deviates.

## Author(s)

T. W. Yee and Kai Huang

`nakagami`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```## Not run: x <- seq(0, 3.2, len = 200) plot(x, dgamma(x, shape = 1), type = "n", col = "black", ylab = "", ylim = c(0,1.5), main = "dnaka(x, shape = shape)") lines(x, dnaka(x, shape = 1), col = "orange") lines(x, dnaka(x, shape = 2), col = "blue") lines(x, dnaka(x, shape = 3), col = "green") legend(2, 1.0, col = c("orange","blue","green"), lty = rep(1, len = 3), legend = paste("shape =", c(1, 2, 3))) plot(x, pnorm(x), type = "n", col = "black", ylab = "", ylim = 0:1, main = "pnaka(x, shape = shape)") lines(x, pnaka(x, shape = 1), col = "orange") lines(x, pnaka(x, shape = 2), col = "blue") lines(x, pnaka(x, shape = 3), col = "green") legend(2, 0.6, col = c("orange","blue","green"), lty = rep(1, len = 3), legend = paste("shape =", c(1, 2, 3))) ## End(Not run) probs <- seq(0.1, 0.9, by = 0.1) pnaka(qnaka(p = probs, shape = 2), shape = 2) - probs # Should be all 0 ```