Abstract
For a sample of size n drawn from a half-Gaussian population with location parameter μ and scale parameter σ, let \( T\, = \,\sqrt n (\bar X - \mu )/S \) where \( \bar X \) is the sample mean and S, the sample standard deviation given by \( (n - 1)S^2 \, = \,\sum {(X_i - \bar X)^2 } \). The tail probability \( G_n (t)\, = \,\{ T \geqslant t\} \) and the density \( f_n (t)\, = \, - dG_n (t)/dt \) are obtained for values of \( t\, \geqslant \,\left( {(n - 1)(n - 2)/2} \right)^{1/2} \). For the special cases n = 2,3,4 explicit expressions for Gn(t) and fn(t) are obtained. For small n and large t, asymptotic tail probabilities for T with Gaussian, half-Gaussian and exponential parent distributions are compared.
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References
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© 1978 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Sirajul Hoq, A.K.M., Ali, M.M., Templeton, J.G.C. (1978). Distribution of Student’s Ratio Based on Half-Gaussian Population. In: Transactions of the Eighth Prague Conference. Czechoslovak Academy of Sciences, vol 8A. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9857-5_27
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DOI: https://doi.org/10.1007/978-94-009-9857-5_27
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