Nakagami: (Weighted) MLE of Nakagami Distribution

Description Usage Arguments Value Author(s) Examples

View source: R/Nakagami.R

Description

Nakagami distribution is characterized by the following probability density function,

f(x;m,Ω) = \frac{2m^m}{Γ(m)Ω^m} x^{2m-1} \exp≤ft( - \frac{m}{Ω} x^2 \right)

where the domain is x \in (0,∞) with two parameters m ≥q 0.5 for shape and Ω > 0 for spread.

Usage

1
Nakagami(x, weight = NULL)

Arguments

x

a length-n vector of values in (0,∞).

weight

a length-n weight vector. If set as NULL, it gives an equal weight, leading to standard MLE.

Value

a named list containing (weighted) MLE of

m

shape parameter m.

omega

spread parameter Ω.

Author(s)

Kisung You

Examples

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#  generate data from half normal
x = abs(stats::rnorm(100))

#  fit unweighted
Nakagami(x)

## Not run: 
# put random weights to see effect of weights
niter = 500
ndata = 200

# generate data as above and fit unweighted MLE
x    = abs(stats::rnorm(ndata))
xmle = Nakagami(x)

# iterate
vec.m     = rep(0,niter)
vec.omega = rep(0,niter)
for (i in 1:niter){
  # random weight
  ww = abs(stats::rnorm(ndata))

  MLE = Nakagami(x, weight=ww)
  vec.m[i]     = MLE$m
  vec.omega[i] = MLE$omega
  if ((i%%10) == 0){
    print(paste0(" iteration ",i,"/",niter," complete.."))
  }
}

# distribution of weighted estimates + standard MLE
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,2))
hist(vec.m, main="shape 'm'")
abline(v=xmle$m, lwd=3, col="red")
hist(vec.omega,  main="spread 'omega'")
abline(v=xmle$omega,  lwd=3, col="blue")
par(opar)

## End(Not run) 

kyoustat/T4mle documentation built on March 26, 2020, 12:09 a.m.