The density of the t-statistic for non-normal distributions
- 1 January 1974
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics
- Vol. 3 (2) , 139-155
- https://doi.org/10.1080/03610927408827113
Abstract
The joint density function of the sample mean and sample variance is recursively derived for samples from a population with density function f where f (x) > 0 cilinost syervi,vheie, everywhere continuous and has certain integral properties. For populations where f does not have these integral properties, this joint density is an approximation. This joint density-function is used to derive the density function of the t-statistic for samples from f. The family of generalized normal density functions is used for an example. The approximation for the t-density is given for that family. For some specific members of the family, the true a probabilities for the approximations are tabled and compared to the results of a simulation study.Keywords
This publication has 8 references indexed in Scilit:
- Student's Distribution Under Non‐Normal SituationsAustralian Journal of Statistics, 1971
- The Power of Student's t-TestJournal of the American Statistical Association, 1965
- A note on criterion robustness and inference robustnessBiometrika, 1964
- The Distribution of "Student's" Ratio for Samples of Two Items Drawn from Non-Normal UniversesThe Annals of Mathematical Statistics, 1939
- The Distribution of “Student'S” Ratio for Non-Normal SamplesJournal of the Royal Statistical Society Series B: Statistical Methodology, 1936
- The Effect of Non-Normality on the t DistributionMathematical Proceedings of the Cambridge Philosophical Society, 1935
- On the Distribution of Student's Ratio for Samples of Three Drawn from a Rectangular DistributionBiometrika, 1933
- The Simultaneous Distribution of Mean and Standard Deviation in Small SamplesThe Annals of Mathematical Statistics, 1932