View source for Graphing a Probability Density

[[Category: Graphs]]

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Graphing the probability density or cumulative probability density of an uncertain variable is easy in Analytica.  You need only select '''Probability Density''' or '''Cumulative Probability''' from the [[Result menu]], or from the result mode dropdown at the top-left corner of a [[result window]].  In these cases, Analytica's GUI automatically knows how to show statistical results when the computed result is a sample indexed by [[Run]].

However, if you compute a [[PDF]] or [[CDF]] histogram yourself, you end up with a 2-D array of histogram points.  To plot this as a histogram, you set up a ''coordinate index''.   This mini-tutorial walks you through the steps.

== Setting up the Data ==

Let's begin by computing some histograph data.  

1. Start Analytica.  In the model object window, title the model "Plotting Histogram Data". Then close the object window.

2. On the diagram, create a chance node, <code>Ch1</code>, and set its definition to
:<code>Pdf(Gamma(10))</code>

3. Press [[image:resultToolbarButton.jpg]] to view the result.

:[[image:histogramExample1.jpg]]

That doesn't look like the [[PDF]] of a [[gamma]] distribution, does it?  In this graph, the bin coordinates (X) are being plotted as one series, and the density values (Y) as a second series.  To plot the PDF, we need to plot X versus Y, rather than plotting X and Y as separate series.

Before doing this, let's examine how the underlying data is organized.

4. Switch to table view, i.e., press the [[image:tableModeIcon.jpg]] button in the graph window.  For easier viewing, pivot the table so that the Step index forms the rows, the DensityIndex the columns.

:[[image:histogramExample2.jpg]]

The values that we wish to plot on the X-values are stored in the first column of the data.  The values we wish to plot on the Y-axis are in the second column.  Hence, the Step index dimensions a set of 2-D data points. Each row of this table represents one point having an (X,Y) coordinate given by the two column values.  

To use each row as a coordinate, we must tell Analytica to use the DensityIndex as the ''coordinate index'' (i.e., the index that dimensions the coordinates of each point).

5. Press the [[image:XYbutton.jpg]] at the top-left corner of the result window.  Select "Use Coordinate Index".

:[[image:Use Coordinate Index dialog.jpg]]

6. Finally, graph the data by pressing [[image:graphModeIcon.jpg]], and we have the desired density graph.

:[[image:histogramExample3.jpg]]

==See Also==
* [[Graph settings]]
* [[Gamma]]()
* [[Cdf and Pdf Functions]]
* [[Probability Distributions]]
* [[Distribution Densities Library]]