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A Generalization of the Childs-Moran Result for Orthoscheme Probabilities

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van der Vaart (1953, 1955) introduced the orthoscheme probability Rn(c1,...,cn−1), meaning the orthant probability of an n-dimensional normal random vector with zero mean and tridiagonal correlation matrix with elements c1,...,cn−1 on the upper diagonal. Childs (1967) conjectured and Moran (1983) proved that the generating function of {Rn(½,...,½)} equals tan z + sin z. This paper derives the generating function of {Rn(,½,...,½)}.
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Keywords: Normal distribution; orthant probability; orthoscheme probability; probability generating function

Document Type: Research Article

Affiliations: Kochi University

Publication date: March 1, 1998

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