#Common Distribution Generators

#Continuous Distributions
#  rnorm(n,mean=0,sd=1)
#  runif(n,min=0,max=1)
#  rgamma(n,shape,rate=1,scale=1/rate)
#  rexp(n,rate=1)
#  rweibull(n,shape,scale=1)
#  rcauchy(n,location=0,scale=1)
#  rt(n,df)

#Discrete Distributions
#  rbinom(n,size,prob)
#  rpois(n,lambda)

#Other Distributions

#Double Exponential
#f(x)=(1/2)exp(-|x|)
rdexp<-function(n) {
  x1<-rgamma(n,shape=1,scale=2)
  x2<-rgamma(n,shape=1,scale=2)
  y<-(x1-x2)/2
  y
}

#Cantaminated (Standard) Normal
#f(x)=(1-p)N(0,1)+pN(0,sd^2)
rcnorm<-function(n,sd=1,p=0) {
  b=rbinom(n,1,p)
  x=(1-b)*rnorm(n,0,1)+b*rnorm(n,0,sd)
  x
}

#Any Distribution
#Simple Example - f(x)=2xI(0<x<1)
rsimp<-function(n) {
  x<-sqrt(runif(n,0,1))
  x
}

#These functions can be used to perform a finite sample
#simulation study that compares the performance of the 
#sample mean and median for cantaminatred (standard) 
#normal distributions.

mysim1<-function(dummy,n,sd=1,p=0) {
  x<-rcnorm(n,sd,p)
  result<-c(mean(x),median(x))
  result
}

mysim<-function(nsims,n,sd=1,p=0) {
  z<-cbind(1:nsims)
  result<-apply(z,1,mysim1,n=n,sd=sd,p=p)
  desc<-c(n,sd,p,nsims)
  names(desc)<-c("n","sd","p","nsims")
  list(data=t(result),desc=desc)
}

mse<-function(asim) {
  mse<-apply(asim$data,2,function(x){mean(x^2)})
  re<-mse[1]/mse[2]
  list(re=re,mse.mean=mse[1],mse.med=mse[2],desc=asim$desc)
}