topic Re: Volume of a 3D gaussian curve in SAS Procedures

Volume of a 3D gaussian curve

deleted_user — Sat, 16 Aug 2008 00:08:35 GMT

I am looking to calculate the volume under a 3D
Gaussian distribution curve. I was wondering if anyone had some code that may help me. Thanks
Chris

Re: Volume of a 3D gaussian curve

mftuchman — Tue, 19 Aug 2008 17:22:26 GMT

What is meant by the volume under a *curve*?

Are you talking about the volume bounded by the x-y plane and the *surface* z=

Re: Volume of a 3D gaussian curve

deleted_user — Tue, 19 Aug 2008 21:28:35 GMT

My bad.. I should have said "cone". Basically, I am asking if I have a volume of air in space and a gas is normally distributed in that 3 dimensional space ( aka cone shape, x,y and z), How do I calculate its volume using SAS. Does that make sense?

Re: Volume of a 3D gaussian curve

mftuchman — Wed, 20 Aug 2008 14:52:52 GMT

Although in principle, the volume is infinite since there is always the probability, albeit infinitesimal, that a particle can be arbitrarily as far as desired. It is a gas, after all. I was still thrown by the cone idea.

Are you suggesting that if (X,Y,Z) are the position of a particular gas particle in space, that X,Y,Z are independent identically distributed normal?

Re: Volume of a 3D gaussian curve

deleted_user — Thu, 21 Aug 2008 15:28:26 GMT

For example, in a 2-d curve we are looking for the area under the curve that is associated with say alpha = 0.90. I am loking for the volume of gas under a cone that is in three dimensional space and normally distributed.

So to answer your question... Yes. The position of a particle is independent identically distributed normal. Thus if we had a cloud of the gas particles, they would form a cloud/cone of gas that has the 3-d shape of a normal curve. I want to find the volume of that gas with 90 % confidence.

I hope I am explaining this better...
Thanks