Discover MakerZone

MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi

Learn more

Discover what MATLAB® can do for your career.

Opportunities for recent engineering grads.

Apply Today

Thread Subject:
cumulative bivariate normal distribution as a function of radius

Subject: cumulative bivariate normal distribution as a function of radius

From: sam Zughni

Date: 18 Aug, 2010 14:35:23

Message: 1 of 2

hi, im stuck on a problem and looking for a bit of help. I have a bivariate normal distribution- mean= [0, 0] , and standard deviation equal in x and y directions. Im trying to find a function or routine that will return the cumulative normal as a function of radius or distance form [0, 0]. i think mvncdf is only good to me for square regions. any clue on how to do this?

Subject: cumulative bivariate normal distribution as a function of radius

From: Roger Stafford

Date: 18 Aug, 2010 17:32:09

Message: 2 of 2

"sam Zughni" <samirzughni@gmail.com> wrote in message <i4gr3b$n37$1@fred.mathworks.com>...
> hi, im stuck on a problem and looking for a bit of help. I have a bivariate normal distribution- mean= [0, 0] , and standard deviation equal in x and y directions. Im trying to find a function or routine that will return the cumulative normal as a function of radius or distance form [0, 0]. i think mvncdf is only good to me for square regions. any clue on how to do this?
- - - - - - - - - -
  You didn't say whether the two distributions are independent. Assuming that they are and assuming that by "cumulative normal" you mean the probability that both distributions lie inside a circle with center (0,0) and radius r, then you can find it by doing the integration. The answer will be

 P(x^2+y^2<=r^2) = 1 - exp(-r^2/(2*sigma^2))

  This comes from the double integral of p(x)*p(y) taken over the circle x^2+y^2<=r^2 where p(x) and p(y) are the two pdf's. You change variables from x and y to polar coordinates and you have integrals that are easy to solve directly by calculus methods.

Roger Stafford

Tags for this Thread

What are tags?

A tag is like a keyword or category label associated with each thread. Tags make it easier for you to find threads of interest.

Anyone can tag a thread. Tags are public and visible to everyone.

Contact us