I've been exploring the Gaussian Blur and have had some good results using Photoshop to get the blurring and color gradient worked in, but that's not a very exacting way of doing the Probability Density. I've come up with a Sine Wave Corrected Color Curves for the Photoshop Color Curves so it can be applied to the Scalar Gray Scale generated by the Gaussian Blur in our test application. It smooths out the colors a little better than the Photoshop Bezier Curves. I just couldn't quite tweak those puppies just right. Below is an example Gray Scale Gradient and Color matching Gradient. Also, you can look at the data in an Excel file I have created. You can get that here: https://members.lotterypost.com/jadelottery/graycolorgradient.xls

The Excel file can explain the image below a little better. From left to right the Gradients are Gray Scale Normal, Gray Scale Inverted, Photoshop Color Scale and Sine Wave Scale.