# What are the scale and location parameters of the Student's t distribution?

I would like advice on how to correctly set the parameters (loc and scale) for the student T distribution that best fits my data of daily stock returns.

I'm pulling random numbers from a student T distribution using python's scipy stats package. I use the number of samples - 1 for the degrees of freedom.

Is it best to use the geometrical mean for the loc parameter and standard deviation or mean absolute deviation for the scale parameter?

I'm using this to run 50,000 simulations on expected portfolio returns in the form of:

return = starting investment + (1-random student T distribution) + annual investment

• Geometric mean of what, exactly? And what do you mean by "correct" or even "use"? – whuber Apr 10 '20 at 14:58
• I mean if I assume a portfolio return follows a student T distribution (which I know it doesn't but it's a better assumption than normal), then I want to 'use' that draw in the return calculation stated above. I mean 'not incorrect' to have the draws make sense in terms of historical returns and volatility. – Jordan Apr 10 '20 at 15:01
• Are you trying to ask how to estimate the parameters of the Student t distribution that best fits your data? – whuber Apr 10 '20 at 15:08
• Yes. I have historical returns. – Jordan Apr 10 '20 at 15:11
• Okay. Please edit your post so that it asks the question you actually need answered! – whuber Apr 10 '20 at 15:15