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The evaluation of general non‐centred orthant probabilities
Author(s) -
Miwa Tetsuhisa,
Hayter A. J.,
Kuriki Satoshi
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00382
Subject(s) - orthant , multivariate normal distribution , multivariate statistics , mathematics , cumulative distribution function , statistics , matrix t distribution , distribution (mathematics) , probability density function , mathematical analysis
Summary. The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non‐centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schläfli and Abrahamson are extended to show that any non‐centred orthant probability can be expressed as differences between at most ( m −1)! non‐centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.