Skip to main content

The evaluation of general non-centred orthant probabilities

Buy Article:

$51.00 plus tax (Refund Policy)

Abstract:

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.

Keywords: Cumulative distribution function; Orthant probability; Orthoscheme probability; Polyhedral cone; Recursive integration

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/1467-9868.00382

Affiliations: 1: National Institute for Agro-Environmental Sciences, Tsukuba, Japan 2: Georgia Institute of Technology, Atlanta, USA 3: Institute of Statistical Mathematics, Tokyo, Japan

Publication date: February 1, 2003

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more