Bernoulli: (Weighted) MLE of Bernoulli Distribution
In kyoustat/T4mle: What the Package Does Using Title Case

Description Usage Arguments Value Author(s) Examples

Bernoulli distribution is characterized by the following probability mass function,

f(x;p) = p^x (1-p)^{1-x}

where the domain is x \in \lbrace 0,1 \rbrace with proportion parameter p \in [0,1].

1	Bernoulli(x, weight = NULL)

`x`	a length-n vector of values \lbrace 0, 1 \rbrace.
`weight`	a length-n weight vector. If set as `NULL`, it gives an equal weight, leading to standard MLE.

a named list containing (weighted) MLE of

p: proportion parameter p.

Kisung You

#  generate data with p=0.5
x = sample(0:1, 50, replace=TRUE, prob=c(0.5,0.5))

#  fit unweighted
Bernoulli(x)

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

# generate data as above and fit unweighted MLE
x    = sample(0:1, ndata, replace=TRUE, prob=c(0.5,0.5))
xmle = Bernoulli(x)

# iterate
vec.p = rep(0,niter)
for (i in 1:niter){
  # random weight
  ww = abs(stats::rnorm(ndata))
  
  # fit
  MLE = Bernoulli(x, weight=ww)
  vec.p[i] = MLE$p
  if ((i%%10) == 0){
    print(paste0(" iteration ",i,"/",niter," complete.."))
  }
}

# distribution of weighted estimates + standard MLE
opar <- par(no.readonly=TRUE)
hist(vec.p, main="proportion 'p'")
abline(v=xmle$p, lwd=3, col="red")
par(opar)

## End(Not run)