How to generate random variable from t distribution with mean and scale

So the question is

How can I take 1000 draws from univariate Student-t distributions with mean = 1.5, scale = 2 and

degrees of freedom nu = 3; 5; 10; 20; 30; 60

[Fanqi Meng]

nu = 3;

sigma = 2;

mu = 1.5;

V = nu * sigma + mu;

x = (-5:0.1:30)';

nct = nctpdf(x,nu,V);

t = tpdf(x,nu);

plot(x,nct,'b-','LineWidth',2)

hold on

plot(x,t,'g--','LineWidth',2)

legend('nct','t')

This is my code. Is this correct?

Answer 1

[Jeff Miller]

I don't see that your code is correct, because it does not take 1,000 draws from anything, which is what you said you want to do.

Actually, it is not clear what you mean by "univariate t-distribution with mean=1.5, scale=2" and any specific df value. Apparently you want a noncentral t-distribution, which is required to give you a nonzero mean. That distribution has a noncentrality parameter and a df parameter, but that is all--there is no separate scale parameter.

Using the Cupid routines, maybe this will give you what you want:

df = 10;  % for example
noncentrality_guess = 0.8;  % This will soon be adjusted to give the desired mean of 1.5.
myt = tNoncentral(df,noncentrality_guess);  % Construct a noncentral t distribution with these parameters.
myt.EstMom(1.5,'fr');  % Adjust the noncentrality parameter to give a distribution mean of 1.5
randvals = myt.Random(1000,1);  % Generate 1,000 draws from the adjusted noncentral t.