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July, 1977 One-Sample $t$-Test When Sampling from a Mixture of Normal Distributions
Austin F. S. Lee, John Gurland
Ann. Statist. 5(4): 803-807 (July, 1977). DOI: 10.1214/aos/1176343904


For the one-sample $t$-test a new form of the exact distribution of the test statistic $t^2$ is obtained when sampling from a distribution which is a mixture of two normal distributions. A numerical example is provided to show that the size of the test can differ greatly when sampling from distributions having the same skewness and kurtosis. Contours of equal size are plotted for a particular case in a certain cross section of the parameter space.


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Austin F. S. Lee. John Gurland. "One-Sample $t$-Test When Sampling from a Mixture of Normal Distributions." Ann. Statist. 5 (4) 803 - 807, July, 1977.


Published: July, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62015
MathSciNet: MR501510
Digital Object Identifier: 10.1214/aos/1176343904

Primary: 62E15
Secondary: 62F05

Keywords: distribution of $t$ , effect of nonnormality , equal probability contours , Mixture of two normal distributions , one-sample $t$-test

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 4 • July, 1977
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