R: The Nakagami Density

Nakagami {nakagami}

R Documentation

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 positive shape parameters.
`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]`.
`p`	vector of probabilities.
`n`	number of observations. If `length(n) > 1`, the length is taken to be the number required.

Details

The Nakagami distribution (Nakagami, 1960) 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 > 0 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.

Sometimes, specifically in radio channels modeling, the parameter m is constrained to m \ge 1/2, but the density is defined for any m > 0 (Kolar et al., 2004).

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.

References

Nakagami, N. 1960. "The M-Distribution, a General Formula of Intensity of Rapid Fading." In Statistical Methods in Radio Wave Propagation: Proceedings of a Symposium Held at the University of California, edited by William C. Hoffman, 3-36. Permagon Press.

Kolar, R., Jirik, R., & Jan, J. (2004). Estimator comparison of the Nakagami-m parameter and its application in echocardiography. Radioengineering, 13(1), 8-12.