Prediction Interval for Poisson Distribution

Question

Dear JMP Communities,

I have data that are count/space.

In my case, (number of events occured / time). As such, it is naturally I would fit these data using Discrete Fit > Poisson.

Afterwards, JMP produces the fitted Poisson with results of Upper/Lower 95% Confidence Interval per below photo.

My question is : How do I get Upper/Lower 95% Prediction Interval?

Thanks for the pointer.

B.r,

Chris

Mark_Bailey · Answer

You are correct - the prediction interval for the lambda is not available in the Distribution platform. Equivalently, I fit an intercept-only Poisson loglinear regression model with the GLM platform to obtain the same estimates, but it does not provide prediction intervals either.

Zappy · Answer

Hi,

Thanks for looking into this question.

I am using JMP ver 14.

I do know there is a "Prediction Interval" option as you have pointed out.

The reason I am questioning that is because, you can see the Confidence Interval calculated are two totally different value (based on 95%).

In my example:

Confidence Interval 95% caculated (based on t density function) is 22.6 to 48.1.

Confidence Interval 95% calculated (based on Poisson density function) is 32.5 to 38.4.

Due to this, it makes me wonder that the Prediction Interval option as you have shown will calculate based on the t density function rather than Poisson.

Hope this brings the question clearly now.

B.r,

Chris

gzmorgan0 · Answer

I don't know which version you are using. Check the inverted red triangle menu next to the variable outline box

Here is an example script:

Names Default To Here( 1 );
dt = Open( "$SAMPLE_DATA/Quality Control/Airport.jmp" );
obj = Distribution( Column( :Delay ) );
obj << Fit Distribution( Poisson );
obj << Prediction Interval(0.95, 1);