Description Usage Arguments Details Value Note Author(s) References See Also Examples
View source: R/family.univariate.R
Estimation of the two parameters of the Nakagami distribution by maximum likelihood estimation.
1 2 
nowarning 
Logical. Suppress a warning? 
lscale, lshape 
Parameter link functions applied to the
scale and shape parameters.
Log links ensure they are positive.
See 
iscale, ishape 
Optional initial values for the shape and scale parameters.
For 
The Nakagami distribution, which is useful for modelling wireless systems such as radio links, can be written
2 * (shape/scale)^shape * y^(2*shape1) * exp(shape*y^2/scale) / gamma(shape)
for y > 0, shape > 0, scale > 0. The mean of Y is sqrt(scale/shape) * gamma(shape+0.5) / gamma(shape) and these are returned as the fitted values. By default, the linear/additive predictors are eta1=log(scale) and eta2=log(shape). Fisher scoring is implemented.
An object of class "vglmff"
(see vglmffclass
).
The object is used by modelling functions such as vglm
,
and vgam
.
The Nakagami distribution is also known as the Nakagamim distribution, where m=shape here. Special cases: m=0.5 is a onesided Gaussian distribution and m=1 is a Rayleigh distribution. The second moment is E(Y^2)=m.
If Y has a Nakagami distribution with parameters shape and scale then Y^2 has a gamma distribution with shape parameter shape and scale parameter scale/shape.
T. W. Yee
Nakagami, M. (1960). The mdistribution: a general formula of intensity distribution of rapid fading, pp.3–36 in: Statistical Methods in Radio Wave Propagation. W. C. Hoffman, Ed., New York: Pergamon.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  nn < 1000; shape < exp(0); Scale < exp(1)
ndata < data.frame(y1 = sqrt(rgamma(nn, shape = shape, scale = Scale/shape)))
nfit < vglm(y1 ~ 1, nakagami, data = ndata, trace = TRUE, crit = "coef")
ndata < transform(ndata, y2 = rnaka(nn, scale = Scale, shape = shape))
nfit < vglm(y2 ~ 1, nakagami(iscale = 3), data = ndata, trace = TRUE)
head(fitted(nfit))
with(ndata, mean(y2))
coef(nfit, matrix = TRUE)
(Cfit < Coef(nfit))
## Not run: sy < with(ndata, sort(y2))
hist(with(ndata, y2), prob = TRUE, main = "", xlab = "y", ylim = c(0, 0.6),
col = "lightblue")
lines(dnaka(sy, scale = Cfit["scale"], shape = Cfit["shape"]) ~ sy,
data = ndata, col = "orange")
## End(Not run)

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