Abstract
Assuming that $X$ has a two-dimensional normal distribution certain conditional distributions of $X$ given that $X$ lies on a hyperbola or a parabola are found. Two of these distributions, related respectively to the parabola and the hyperbola, resemble the von Mises distribution, which can be obtained as a conditional distribution of $X$ given that $X$ lies on a circle. It is, however, proved that the assumptions leading to the conditional distribution in the hyperbolic case are not analogous to those leading to the von Mises distribution.
Citation
P. Blaesild. "Conditioning with Conic Sections in the Two-Dimensional Normal Distribution." Ann. Statist. 7 (3) 659 - 670, May, 1979. https://doi.org/10.1214/aos/1176344686
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