Kernel Density Smoothing

new to Analytica 4.4

This page to describe the new "Smoothing" option on the Uncertainty Settings→Probability Density pane: What it is, how it smooths. Maybe some warning about how smoothing causes an increase in the apparent variance. Why it may be preferable to using a histogram method. How the PDF function can be used in unusual cases where you want more control -- a custom smoothing factor, fewer or more plotted points, etc.

Written assuming reader understands Monte Carlo samples, the basics of continuous probability distributions, but doesn't know what KDE is.

In Analytica 4.4, if you go to the Uncertainty Options dialog (an option under the Results drop down menu), and select Probability Density from the Analysis option drop down menu, you will see the Probability Density panel has changed. There are two new radio buttons: "Histogram" and "Smoothing."

"Histogram" will give you a Probability Density Function (PDF) graph which is a histogram, or step function, as before.

However, "Smoothing" will give you a smoothed, continuous curve for your PDF. This is a new feature in 4.4.

When you generate a random variable, either from a built in distribution, or from a sequence of calculations based on random distributions, there is an underlying theoretical PDF. Before 4.4, you are able to graph this PDF as a histogram, and able to use this histogram for further calculations. The histogram gives you an indication of what the underlying PDF is, but can be quite sensitive to your random sampling methodology.

If you want to use the ramdom sample to get an idea of the underlying PDF,