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Thread Subject:
mvncdf over a circle

Subject: mvncdf over a circle

From: jorge Sierra

Date: 2 Dec, 2010 12:18:05

Message: 1 of 4

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

Subject: mvncdf over a circle

From: Roger Stafford

Date: 2 Dec, 2010 17:22:04

Message: 2 of 4

"jorge Sierra" <timgriguol@hotmail.com> wrote in message <id82pt$j0b$1@fred.mathworks.com>...
> 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
- - - - - - - - -
  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

Subject: mvncdf over a circle

From: Peter Perkins

Date: 2 Dec, 2010 18:08:42

Message: 3 of 4

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.

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.

Subject: mvncdf over a circle

From: Roger Stafford

Date: 2 Dec, 2010 19:03:06

Message: 4 of 4

Peter Perkins <Peter.Perkins@MathRemoveThisWorks.com> wrote in message <id8nba$mp4$1@fred.mathworks.com>...
> 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.
>
> 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.
- - - - - - - -
  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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