Comparing Beta Density Functions
This applet faciliates the comparison of shapes of beta probability density functions with different values of parameters alpha and beta. For any of the color-coded curves, change its values of alpha and beta in the text box and press the "Return" key to update the graphs. When this page loads it displays the three beta density functions in Figure 4.17. Change the parameters in the text boxes to explore how the parameters of the beta density function affect its shape.
Note: There is currently a problem with the display that prevents values of alpha or beta less than 1. This will be corrected.
Mathematical Details
The probability density function for the beta distribution is defined by
where
where
The mean of the beta distribution is defined as
and the variance is defined as
HTML and Param Tags
Below is sample code to place this applet on an html page. The codebase is specified relative to the html file and does not need to be "../../lib" as below.
<applet code="com.bolderstats.density.BetaCompare.class"
width="500" height="300"
codebase="../../lib" archive="bolderstats_obf.jar,jmsl_obf.jar">
</applet>
- a1, a2, and a3
- Value of the a or alpha parameter of the beta distribution for the three curves, respectively. The default values are, respectively, 2, 3, and 5
- b1, b2, and b3
- Value of the b or beta parameter of the beta distribution for the three curves, respectively. The default valure are, respectively, 2, 3, and 3.