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bivariate normal cdf #2356

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@bob-carpenter

Description

@bob-carpenter

Summary:

Add a function to compute the bivariate normal cdf.

Description:

For size 2 vectors y and mu and 2 x 2 covariance matrix Sigma, compute

bivar_normal_cdf(y, mu, Sigma)

  = INT_{u < y}  multinormal_pdf(u, mu, Sigma) d.u

where u is also a 2-vector and u < y is defined componentwise as u[1] < y[1] && u[2] < y[2].

There could also be a parameterization where covariance is given in terms of two scale parameters and a correlation parameter.

Additional Info:

This paper is often cited for an algorithm:

  • Boys, R.J., 1989. Algorithm AS R80: A remark on Algorithm AS 76: An integral useful in calculating noncentral t and bivariate normal probabilities. Journal of the Royal Statistical Society. Series C (Applied Statistics), 38(3), pp.580-582. https://www.jstor.org/stable/2347755

Current Version:

v2.16.0

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