Nakagami Distribution

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

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.

Value

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

Author

T. W. Yee and Kai Huang

Details

See nakagami for more details.

See also

nakagami.

Examples

if (FALSE)  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)")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
lines(x, dnaka(x, shape = 1), col = "orange")
#> Error: object 'x' not found
lines(x, dnaka(x, shape = 2), col = "blue")
#> Error: object 'x' not found
lines(x, dnaka(x, shape = 3), col = "green")
#> Error: object 'x' not found
legend(2, 1.0, col = c("orange","blue","green"), lty = rep(1, len = 3),
       legend = paste("shape =", c(1, 2, 3)))
#> Error in (function (s, units = "user", cex = NULL, font = NULL, vfont = NULL,     ...) {    if (!is.null(vfont))         vfont <- c(typeface = pmatch(vfont[1L], Hershey$typeface),             fontindex = pmatch(vfont[2L], Hershey$fontindex))    .External.graphics(C_strWidth, as.graphicsAnnot(s), pmatch(units,         c("user", "figure", "inches")), cex, font, vfont, ...)})(dots[[1L]][[1L]], cex = dots[[2L]][[1L]], font = dots[[3L]][[1L]],     units = "user"): plot.new has not been called yet

plot(x, pnorm(x), type = "n", col = "black", ylab = "",
     ylim = 0:1, main = "pnaka(x, shape = shape)")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
lines(x, pnaka(x, shape = 1), col = "orange")
#> Error: object 'x' not found
lines(x, pnaka(x, shape = 2), col = "blue")
#> Error: object 'x' not found
lines(x, pnaka(x, shape = 3), col = "green")
#> Error: object 'x' not found
legend(2, 0.6, col = c("orange","blue","green"), lty = rep(1, len = 3),
       legend = paste("shape =", c(1, 2, 3)))  # \dontrun{}
#> Error in (function (s, units = "user", cex = NULL, font = NULL, vfont = NULL,     ...) {    if (!is.null(vfont))         vfont <- c(typeface = pmatch(vfont[1L], Hershey$typeface),             fontindex = pmatch(vfont[2L], Hershey$fontindex))    .External.graphics(C_strWidth, as.graphicsAnnot(s), pmatch(units,         c("user", "figure", "inches")), cex, font, vfont, ...)})(dots[[1L]][[1L]], cex = dots[[2L]][[1L]], font = dots[[3L]][[1L]],     units = "user"): plot.new has not been called yet

probs <- seq(0.1, 0.9, by = 0.1)
pnaka(qnaka(p = probs, shape = 2), shape = 2) - probs  # Should be all 0
#> [1] -3.427853e-06 -1.984841e-05  2.767343e-05  9.541734e-06  1.030903e-06
#> [6]  4.864279e-06 -5.028646e-07 -1.703812e-05 -1.239174e-08