Help with 3D Gaussian Distribution Formula in Excel?

Hi Everyone,

I am looking for some help! I am not a statistician but use 3 Gaussian distributions in my work which is all Excel based. I currently use the following formula produce a normally distributed 3D shape in Excel that produces the attached surface plot:-

I use Excel Solver to alter the a,b,c,x0 and y0 to achieve the best fit to the actual data (Pictures attached).

What I would like some help with is how I can alter this formula to add 'skew' in either the x0 or y0 direction so I can get a better fit to the actual shape…..

Re: Help with 3D Gaussian Distribution Formula in Excel?

Two Comments:

1. I believe you have a bivariate Gaussian distribution which you plot out the estimated joint density. To estimate the parameter you can use different methods like the MLE which has closed form solution and thus do not need to use numerical solver.

2. Ordinary bivariate Gaussian distribution is symmetric. The marginal distribution of either component is just univariate Gaussian therefore the projection of the joint density in either x or y direction should produce a bell-shaped figure again. Of course due to possible correlation in general it will be an ellipse from top view. And the most important thing is to define "skewness" in multivariate sense.

One can always have different way to generalize the normal distribution, like