Probability Density Tail Area
This add-in plots and compares tail areas for a wide range of probability density functions. Such comparisons can be helpful when interpreting frequentist p-values or Bayesian one-sided posterior probabilities. The add-in is also a convenient way to learn the shape and form of the most commonly used densities in probability and statistics.
After installing the add-in by dragging the .jmpaddin file onto your JMP window, you must create a small JMP table describing the densities to be plotted. Each row corresponds to a different density and several columns with specific names are required to fully specify each density and tail cut point. Once the table is set up, make sure it is in focus, then click Add-Ins > Probability Density Tail Area.
Several example tables are attached, and the one named pdta_normal.jmp produces the following output. It illustrates the equivalence of a one-sided p-value and Bayesian posterior probability of having the wrong sign under normal inference on a mean.
You can change the cutoff values dynamically in three different ways: 1. Click and drag the vertical dotted reference lines. 2. Enter values in the Cut boxes. 3. Click and drag the diamonds in the slider bars.
The input table must contain the following columns:
- density (used as a label in the plots)
- form (keyword for the kind of density, see list below)
- tail (right or left)
- cut (numeric values at which to draw the initial cut points)
In addition, you must specify numeric columns corresponding to the parameters of the desired densities. The following excerpt from the add-in's JSL code shows which densities are currently available along with the parameter names that go with them:
required = associativearray();
required["beta"] = {"alpha","beta","theta","sigma"};
required["betabinomial"] = {"p","n","delta"};
required["binomial"] = {"p","n"};
required["cauchy"] = {"mu","sigma"};
required["chisquare"] = {"df","noncentrality"};
required["exp"] = {"theta"};
required["f"] = {"dfnum","dfden","noncentrality"};
required["frechet"] = {"mu","sigma"};
required["gamma"] = {"alpha","scale","threshold"};
required["gengamma"] = {"mu","sigma","lambda"};
required["gammapoisson"] = {"lambda","sigma"};
required["glog"] = {"mu","sigma","lambda"};
required["hypergeometric"] = {"s","k","n"};
required["johnsonsb"] = {"gamma","delta","theta","sigma"};
required["johnsonsl"] = {"gamma","delta","theta","sigma"};
required["johnsonsu"] = {"gamma","delta","theta","sigma"};
required["lev"] = {"mu","sigma"};
required["loggengamma"] = {"mu","sigma","lambda"};
required["logistic"] = {"mu","sigma"};
required["loglogistic"] = {"mu","sigma"};
required["lognormal"] = {"mu","sigma"};
required["negbinomial"] = {"p","n"};
required["normal"] = {"mu","sigma"};
required["poisson"] = {"lambda"};
required["sev"] = {"mu","sigma"};
required["shash"] = {"gamma","delta","theta","sigma"};
required["t"] = {"mu","sigma","df"};
required["weibull"] = {"shape","scale","threshold"};
Refer to the JSL documentation for further details about these densities and parameters.