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On the computation of a bivariate $ t$-distribution


Authors: D. E. Amos and W. G. Bulgren
Journal: Math. Comp. 23 (1969), 319-333
MSC: Primary 65.25; Secondary 62.00
DOI: https://doi.org/10.1090/S0025-5718-1969-0242348-0
MathSciNet review: 0242348
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Abstract: The cumulative bivariate $ t$-distribution associated with random variables $ {T_1} = {X_1}/{(S/k)^{1/2}}$, $ {T_2} = {X_2}/{(S/k)^{1/2}}$ is considered where $ {X_1}$, $ {X_2}$ are bivariate normal with correlation coefficient $ \rho $ and $ S$ is an independent $ {\chi^2}$ random variable with $ k$ degrees of freedom. Representations in terms of series and simple, one-dimensional quadratures are presented together with efficient computational procedures for the special functions used in numerical evaluation.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1969-0242348-0
Article copyright: © Copyright 1969 American Mathematical Society

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