LogitNormal: (Weighted) MLE of Logit-Normal Distribution

In kyoustat/T4mle: What the Package Does Using Title Case

Description

Logit-Normal distribution is characterized by the following probability density function,

f(x;μ, σ) = \frac{1}{σ √{2π}} \frac{1}{x(1-x)} \exp ≤ft\lbrace - \frac{(\textrm{logit}(x)-μ)^2}{2σ^2} \right\rbrace

where the domain is x \in \mathbf{R} with parameters for location μ \in \mathbf{R} and dispersion σ^2 \in (0,∞). \textrm{logit}(x) is a logit function, i.e., \textrm{logit}(x) = \log(x/(1-x)).

Usage

LogitNormal(x, weight = NULL)

Arguments

x	a length-n vector of values in (0,1).
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

mu

location μ.

sigma

standard deviation σ.

Author(s)

Kisung You

Examples

#  generate data from Unif(0,1)
x = stats::runif(100)

#  fit unweighted
LogitNormal(x)

## Not run: 
# put random weights to see effect of weights
niter = 1000
ndata = 200

# generate data as above and fit unweighted MLE
x    = stats::runif(ndata)
xmle = LogitNormal(x)

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

  MLE = LogitNormal(x, weight=ww)
  vec.mu[i]  = MLE$mu
  vec.sig[i] = MLE$sigma
  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.mu,  main="location 'mu'")
abline(v=xmle$mu, lwd=3, col="red")
hist(vec.sig, main="dispersion 'sigma'")
abline(v=xmle$sigma, lwd=3, col="blue")
par(opar)

## End(Not run) 

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