What does the rt() function in R generates?

Question

At first, I thought I understood what will the rt() function in R generate - I thought it generates random t-valuesfrom the specified t-distribution.

For example, this function tdist <- rt(10000,19) generates, I interpreted, 10,000 t-values from a t-distribution that based on n=20 (df=19), with mean=0 and standard deviation=1.

Is that the case, or does it generate average scores (means) that are to be found under the specified t-distribution?

If the latter is the case, how can I generate from a t-distribution 10,000 times a n=20 sample with specifications mean=0, sd=1?

Thank you in advance!

Answer 1

Yes, rt(n, df) generates n random samples from t-distribution with df degrees of freedom.

with mean=0 and standard deviation=1.

True about distribution mean (though sampled mean would be different), but standard deviation for t-distribution is ALWAYS not a 1, but a bit larger, equal to sqrt(df/(df-2)), sqrt(19/17)=1.057 in your case.

Lets put some code (MS R open 3.5.3, Win10 x64)

q <- rt(10000, 19)
mean(q)

prints

-0.008859063

sd(q)

prints

1.049836

and

hist(q)

plots