Nakagami: The Nakagami Density

Description

Density, distribution function, quantile function and random generation for the Nakagami distribution with parameters shape and scale.

Usage

dnaka(x, shape, scale, log = FALSE)
pnaka(q, shape, scale, lower.tail = TRUE, log.p = FALSE)
qnaka(p, shape, scale, lower.tail = TRUE, log.p = FALSE)
rnaka(n, shape, scale)

Arguments

x, q

vector of quantiles.

shape

vector of shape parameters greater than 1/2.

scale

vector of positive scale parameters.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are $P[X \le x]$ otherwise, $P[X > x]$.

vector of probabilities.

number of observations. If length(n) > 1, the length is taken to be the number required.

Value

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

The length of the result is determined by n for rnaka, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result.

Details

The Nakagami distribution with shape $m$ and scale $\Omega$ has density $$2m^m/{\Gamma(m)\Omega^m} x^(2m-1)e^(-m/\Omega x^2)$$ for $x \ge 0$, $m \ge 1/2$ and $\Omega > 0$.

If $Y$ is Gamma distributed with $shape = m$ and $rate = m/\Omega$ then $X = \sqrt Y$ is Nakagami distributed with $shape = m$ and $scale = \Omega$.

References