Sampling Distribution

T distribution

df.vec = seq(1,27,length.out = 9)
par(mfrow=c(3,3))
for (i in 1:9) {
  plot(density(rt(100,df=df.vec[i])),
       main = sprintf("df=%s",df.vec[i])
       )
}

Chi-Squre distribution

df.vec = seq(1,27,length.out=9)
par(mfrow=c(3,3))
for (i in 1:9) {
  plot(density(rchisq(100,df=df.vec[i])),
       main = sprintf("df=%s",df.vec[i]))
}

F distribution

df1.vec = seq(1,27,length.out=9)
df2.vec = seq(1,27,length.out=9)
par(mfrow=c(3,3))
for (i in 1:9) {
  plot(density(rf(100,df1=df1.vec[i],df2=df2.vec[1])),
       main = c(sprintf("df1=%s",df1.vec[i]), sprintf("df2=%s",df2.vec[1])))
}

par(mfrow=c(3,3))
for (i in 1:9) {
  plot(density(rf(100,df1=df1.vec[1],df2=df2.vec[i])),
       main = c(sprintf("df1=%s",df1.vec[1]), sprintf("df2=%s",df2.vec[i])))
}

par(mfrow=c(3,3))
for (i in 1:9) {
  plot(density(rf(100,df1=df1.vec[i],df2=df2.vec[i])),
       main = c(sprintf("df1=%s",df1.vec[i]), sprintf("df2=%s",df2.vec[i])))
}