# nakagami

## Overview

An `R`-package for the Nakagami distribution.

## Installation

Use the following command from inside `R`:

``````# install.packages("devtools")
devtools::install_github("JonasMoss/nakagami")``````

## Usage

The density function is `dnaka`, the probability distribution is `pnaka`, the quantile function is `qnaka` and random deviate generator is `rnaka`. Use them just like the `*gamma` functions in the `stats` package.

``````set.seed(313)
x = seq(0, 3, by = 0.01)
hist(nakagami::rnaka(10^5, shape = 4, scale = 2), freq = FALSE, breaks = "FD")
lines(x, nakagami::dnaka(x, shape = 4, scale = 2), type = "l", lwd = 2)``````

## Note

All of these functions are implemented in the `R` package `VGAM`. As of `VGAM` version 1.1-2, the implementations in `nakagami` are faster, more thoroughly tested, and use a standardized set of arguments following the template of `dgamma` et cetera.

The `rnaka` of `nakagami` is much faster than the `rnaka` of `VGAM`:

``````#install.packages("VGAM")

microbenchmark::microbenchmark(nakagami::rnaka(100, 2, 4),
VGAM::rnaka(100, 4, 2))
#> Unit: microseconds
#>                        expr    min      lq      mean median      uq
#>  nakagami::rnaka(100, 2, 4)  265.9  303.45   553.702  352.6  430.25
#>      VGAM::rnaka(100, 4, 2) 2028.3 2355.35 17558.350 2670.4 3040.85
#>        max neval
#>    15697.2   100
#>  1480179.6   100``````

And the quantile function of `nakagami` is slightly faster.

``````p = 1:10/11
microbenchmark::microbenchmark(nakagami::qnaka(0.01, 10, 4),
VGAM::qnaka(0.01, 4, 10))
#> Unit: microseconds
#>                          expr   min     lq     mean median     uq      max
#>  nakagami::qnaka(0.01, 10, 4) 143.6 170.10 2117.254 201.65 293.25 183790.6
#>      VGAM::qnaka(0.01, 4, 10) 345.9 389.55  565.839 464.65 585.10   2706.5
#>  neval
#>    100
#>    100``````

Moreover, `VGAM::qnaka` fails to implement the standard argument `log.p` and `VGAM::rnaka` uses the non-standard arguments `Smallno` and `...`.

## How to Contribute or Get Help

If you encounter a bug, have a feature request or need some help, open a Github issue.

This project follows a Contributor Code of Conduct.

## 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, June 18–20, 1958, edited by William C. Hoffman, 3–36. Permagon Press. https://doi.org/10.1016/B978-0-08-009306-2.50005-4.

• Yee TW (2010). “The VGAM Package for Categorical Data Analysis.” Journal of Statistical Software, 32(10), 1–34. https://www.jstatsoft.org/v32/i10/.