Tiago <[email protected]> asks how to simulate data from Student's t
distribution:
> I would like to generate a new variable called "x", in which "x" has a
> t-distribution with n-3 degrees of freedom (where n is the number of new
> generated observations), a mean "m" and a standard deviation, "sd", that
> is:
>
> x ~ t-distribution[n-3 df] (m, sd)
>
> How do I obtain a set of 100 new observations assuming that m=0.4 and
> sd=0.05 using Stata?
>
> I will be very grateful for any help.
Here is a do-file that will simulate a dataset from Student's t distribution
with the requested degrees of freedom, mean, and standard deviation:
***** BEGIN: sim-t.do
// set the random number seed for reproducing the simulated values
set seed 12345
// parameters for the data generating process
local n 100 // sample size
local m 0.4 // mean
local sd 0.05 // standard deviation
// assuming we are starting with an empty dataset, set the sample size
set obs `n'
gen x = `m' + `sd'*invttail(`n'-3, uniform())
***** END: sim-t.do
We can use -invttail()- since the t distribution is continuous and symmetric
about 0.
Note that we could use -invnormal()- instead since the degrees of freedom, 97,
are so much greater than 30 (where the differences between the two CDF's are
practically indistinguishable).
--Jeff
[email protected]
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