How to use Ratio or Cauchy Distribution in JMP to analyze capability

mcastner

I have 2 data sets of continuous values that are combined together to form a ratio, such as a contrast ratio.  I am familiar with fitting multiple distributions but I have been told by a colleague that the best way to analyze this ratio data for capability is to fit it to a Ratio or Cauchy distribution.  It is unclear to me if there is a way to do this in JMP 14.  

ian_jmp

You should be able to fit a Cauchy distribution with the Nonlinear platform, though as usual, you may have to be careful about the starting values you use.

 

The attached table might get you started. It has some data (in this case generated randomly from a Cauchy distribution with a median of zero), then a formula column for the negative logLikelihood that is used by Nonlinear.

 

The end result is shown below, where the fit is the red line:

 

Fit_cauchy.jmp