, Volume 69, Issue 2, pp 175–183

Examples of non-normal observations for which a studentized sample mean has a student’s T-distribution


    • Department of StatisticsUniversity of Connecticut Storrs
  • Bhargab Chattopadhyay
    • Department of StatisticsUniversity of Connecticut Storrs

DOI: 10.1007/BF03263555

Cite this article as:
Mukhopadhyay, N. & Chattopadhyay, B. METRON (2011) 69: 175. doi:10.1007/BF03263555


Statistical methodologies and their practice often rely upon tests and confidence interval procedures based on Studentized sample means of independent observations from a normal parent population and their Student’s t distributions. This is specially so when the sample size n is small. An unmistakable impression one is left with, whether implied or not, is that such exact Student’s t distributions may not be valid when the observations are dependent or non-normal. We show that one cannot discard the possibility of an exact Student’s t distribution for a Studentized sample mean, or its suitable multiple, simply because the observations may be dependent or non-normal. In arriving at this conclusion, we have uncovered a very interesting and seemingly unknown feature (Theorem 2.1) of an n-dimensional multivariate t distribution with equi-correlation p, arbitrary degree of freedom v, and arbitrary n.

Key Words

Dependent dataEqui-correlated tMulti-modal dataMultivariate CauchyMultivariate FMultivariate tNon-normal dataPeaked data

Copyright information

© Sapienza Università di Roma 2011