Simulating the Central Limit Thereom

[Chinmay Sharma]

I am attempting to write a program,wherein I wish to simulate the Central Limit Theorem (the result that the distribution of sample averages less the true mean and scaled by the standard deviation has a standard normal limiting distribution). As a result, I wrote the following code:

program normal10, rclass
drop _all
quietly set obs 10
generate x= rnormal(0,1)
sum x
return scalar meanforonedraw=r(mean)
return scalar stdevforonedraw=r(sd)
end
simulate Zn=(10^0.5)*(r(meanforonedraw)/r(stdevforonedraw)), reps(1000): normal10

I obtain the error message: "Expression must be bound in parantheses". I fail to see how I have not done that. Any help is much appreciated.

[Clyde Schechter]

The error message means exactly what it says, and the syntax shown at -help simulate- is quite clear: the expression after the equals sign has to be bound in parentheses. Your expression has various parentheses contained in it, but you have to wrap the whole thing in partentheses:

simulate Zn= ((10^0.5)*(r(meanforonedraw)/r(stdevforonedraw))), reps(1000): normal10

That said, this is a pretty minimalist demonstration of the central limit theorem, as your underlying distribution is itself already normal. In fact, this result doesn't even require the central limit theorem: you can get it from the fact that the normal distribution family is stable. It's a lot more eye-opening if you do this with a distribution that is very different from normal, for example using an exponential distribution.

[Chinmay Sharma]

Thanks a lot Clyde. I plan to compare this to when the parent distributions are not normal. This is just the first part of the simulation. The second simulation is going to make use of a Bernoulli RV. Really appreciate it.

[JOSE LIMA]

Very usefull