This page contains related R codes for STAT 51100 Section 010. This page is for Chapter 5, sampling distribution of some statistics.

The following simulate 10,000 gamma distribution with \(\alpha=2\) and \(\beta=1\).

set.seed(10000)
x<-rgamma(10000, shape=2, scale=1)
hist(x, freq=F, main='Histogram of 10,000 Gamma(2, 1) observations')

We will then generate 1,000 data sets with different sample sizes (2, 4, 10, 20, 25, 30, 35, 50, 100, 200, 500) to investigate the distribution of \(\overline{X}\).

## $breaks
##  [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
## 
## $counts
##  [1]  28 121 215 210 172 103  68  45  23   7   6   2
## 
## $density
##  [1] 0.056 0.242 0.430 0.420 0.344 0.206 0.136 0.090 0.046 0.014 0.012
## [12] 0.004
## 
## $mids
##  [1] 0.25 0.75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 4.75 5.25 5.75
## 
## $xname
## [1] "apply(datamat, 2, \"mean\")"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## NULL

## $breaks
##  [1] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
## 
## $counts
##  [1]   6  88 214 2