# (1) basic fit of a normal distribution with maximum likelihood estimation
#
x1<-c(6.4,13.3,4.1,1.3,14.1,10.6,9.9,9.6,15.3,22.1,13.4,
13.2,8.4,6.3,8.9,5.2,10.9,14.4)
mledist(x1,"norm")
# (2) defining your own distribution functions, here for the Gumbel distribution
# for other distributions, see the CRAN task view dedicated to probability distributions
dgumbel<-function(x,a,b) 1/b*exp((a-x)/b)*exp(-exp((a-x)/b))
mledist(x1,"gumbel",start=list(a=10,b=5))
# (3) fit a discrete distribution (Poisson)
#
x2<-c(rep(4,1),rep(2,3),rep(1,7),rep(0,12))
mledist(x2,"pois")
mledist(x2,"nbinom")
# (4) fit a finite-support distribution (beta)
#
x3<-c(0.80,0.72,0.88,0.84,0.38,0.64,0.69,0.48,0.73,0.58,0.81,
0.83,0.71,0.75,0.59)
mledist(x3,"beta")
# (5) fit frequency distributions on USArrests dataset.
#
x4 <- USArrests$Assault
mledist(x4, "pois")
mledist(x4, "nbinom")
# (6) fit a continuous distribution (Gumbel) to censored data.
#
d1<-data.frame(
left=c(1.73,1.51,0.77,1.96,1.96,-1.4,-1.4,NA,-0.11,0.55,0.41,
2.56,NA,-0.53,0.63,-1.4,-1.4,-1.4,NA,0.13),
right=c(1.73,1.51,0.77,1.96,1.96,0,-0.7,-1.4,-0.11,0.55,0.41,
2.56,-1.4,-0.53,0.63,0,-0.7,NA,-1.4,0.13))
mledist(d1,"norm")
dgumbel<-function(x,a,b) 1/b*exp((a-x)/b)*exp(-exp((a-x)/b))
pgumbel<-function(q,a,b) exp(-exp((a-q)/b))
mledist(d1,"gumbel",start=list(a=0,b=2),optim.method="Nelder-Mead")
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