, Volume 69, Issue 2, pp 175183
First online:
Examples of nonnormal observations for which a studentized sample mean has a student’s Tdistribution
 Nitis MukhopadhyayAffiliated withDepartment of Statistics, University of Connecticut Storrs Email author
 , Bhargab ChattopadhyayAffiliated withDepartment of Statistics, University of Connecticut Storrs
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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 nonnormal. 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 nonnormal. In arriving at this conclusion, we have uncovered a very interesting and seemingly unknown feature (Theorem 2.1) of an ndimensional multivariate t distribution with equicorrelation p, arbitrary degree of freedom v, and arbitrary n.
Key Words
Dependent data Equicorrelated t Multimodal data Multivariate Cauchy Multivariate F Multivariate t Nonnormal data Peaked data Title
 Examples of nonnormal observations for which a studentized sample mean has a student’s Tdistribution
 Journal

METRON
Volume 69, Issue 2 , pp 175183
 Cover Date
 201108
 DOI
 10.1007/BF03263555
 Print ISSN
 00261424
 Online ISSN
 2281695X
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Dependent data
 Equicorrelated t
 Multimodal data
 Multivariate Cauchy
 Multivariate F
 Multivariate t
 Nonnormal data
 Peaked data
 Authors

 Nitis Mukhopadhyay ^{(1)}
 Bhargab Chattopadhyay ^{(1)}
 Author Affiliations

 1. Department of Statistics, University of Connecticut Storrs, Connecticut Storrs, CT 062694120, U.S.A