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mvncdf over a circle
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jorge Sierra
Dec 2, 2010, 7:18:05 AM12/2/10
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Hi,
I am trying to calculate the cumulative density function of a bivariate normal distribution but over a circle instead of over a rectangle, as the function mvncdf solves.
Could anyone help me?
Thank you very much
I am trying to calculate the cumulative density function of a bivariate normal distribution but over a circle instead of over a rectangle, as the function mvncdf solves.
Could anyone help me?
Thank you very much
Roger Stafford
Dec 2, 2010, 12:22:04 PM12/2/10
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"jorge Sierra" <timgr...@hotmail.com> wrote in message <id82pt$j0b$1...@fred.mathworks.com>...- - - - - - - - -
This is the equivalent of integrating the bivariate density of two independent random variables with standard normal distributions but over an expanding ellipse. If the ellipse turns out to be an expanding circle centered at the origin, the integration is very easy. Otherwise you face a much more difficult integration that very likely requires the use of numerical double integration.
This is the equivalent of integrating the bivariate density of two independent random variables with standard normal distributions but over an expanding ellipse. If the ellipse turns out to be an expanding circle centered at the origin, the integration is very easy. Otherwise you face a much more difficult integration that very likely requires the use of numerical double integration.
Roger Stafford
Peter Perkins
Dec 2, 2010, 1:08:42 PM12/2/10
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On 12/2/2010 7:18 AM, jorge Sierra wrote:
> I am trying to calculate the cumulative density function of a bivariate
> normal distribution but over a circle instead of over a rectangle, as
> the function mvncdf solves.
> I am trying to calculate the cumulative density function of a bivariate
> normal distribution but over a circle instead of over a rectangle, as
> the function mvncdf solves.
You may find something suitable among the MATLAB functions at Alan
Genz's website:
http://www.math.wsu.edu/faculty/genz/software/software.html
His published papers were the work on which MVNCDF was based. Hope this
helps.
Roger Stafford
Dec 2, 2010, 2:03:06 PM12/2/10
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Peter Perkins <Peter....@MathRemoveThisWorks.com> wrote in message <id8nba$mp4$1...@fred.mathworks.com>...
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It looks as though the 'mvnlps' function in the site Peter recommended does just what you want. In your case the ellipsoid would be a two-dimensional circle with expanding radius R. Here is what its description says:% MVNLPS Multivariate Normal Distribution Value for an ellipsoid.
% MVNVAL = MVNLPS( MU, SIGMA, Q, E, R, RE ) computes
% an MVN value to relative accuracy RE for an ellipsoid centered
% at Q with radius R and positive semi-definite ellipsoid matrix E:
% MVNVAL = PROB( ( X - Q )'E ( X - Q ) < R^2 )
% SIGMA is a positive definite covariance matrix for a multivariate
% normal (MVN) density with mean MU. MU and Q must be column vectors.
Roger Stafford
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