Hello, I'm having problems to build an approximate distribution for the mean and the standard devistion using a results from a sampling distribution with number of samples=10. Should I use t-student distribution for the mean and chi-square for the standard deviation? Please I would appreciate a response using some Matlab routines from the statistical toolbox.

Maybe I should explain the context of the problem. I'm having a particle size distribution (PSD) with a mean radius and a PSD standard deviation. I'm taking a sample of that distribution by a scanning electron microscopy and i want to use this sampling information as a prior distribution for such parameters (mean radius and PSD standard deviation). I can find confidence intervals for a 10-particle sample but I need an approximate distribution. So I want someone could give me an advise about generating these approximate distributions. For a sample of more than 30 I supposed normal-shape distributions but I guess that's no longer valid for small samples. I hope this could help to understand a little bit more my problem.

Thank you very much.