Nakagami: The Nakagami Density
In JonasMoss/nakagami: Functions for the Nakagami Distribution

Description Usage Arguments Details Value References See Also

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

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)

`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 ≤ 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.

The Nakagami distribution (Nakagami, 1960) with shape m and scale Ω has density

2m^m/{Γ(m)Ω^m} x^(2m-1)e^(-m/Ω x^2)

for x ≥ 0, m > 0 and Ω > 0.

If Y is Gamma distributed with shape = m and rate = m/Ω then X = √ Y is Nakagami distributed with shape = m and scale = Ω.

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

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.

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.

The Gamma distribution is closed related to the Nakgami distribution.

JonasMoss/nakagami documentation built on Sept. 17, 2021, 7:36 p.m.