What's the right interpretation of the Homogeneity Test in Recurrence Analysis?

[#1]

Hello Community!

One quick question, JMP documentation states that (in recurrence analysis): Test Homogeneity Tests if the process is homogeneous. 

and JMP also says that this tests if the scale model is constant 1, but what does it mean with being '1'? 

So if we are looking for a good fit, meaning that our Y's (predicted cumulative repairs) are close to Y(actual data),  what P-value should we look for?

if the scale parameter is 1 (H0), then the rate parameter is also 1, and the interarrival distribution is ID exponential (e^x), but is this any good for our objective? (good fit) 

Thanks in advance!

[#2 · Accepted solution]

Take a look at formulas here, Fit Model in Recurrence Analysis, for Homogeneous Poisson Process (HPP) and other non-homogeneous Poisson processes (NHPP). The intensity function of HPP is not a function of time t. The intensity functions of NHPP are functions of time t.

So the homogeneity test is to see whether the intensity function (failure rate) is changing over time.

The homogeneity test for Power NHPP is to test beta == 1. The test for Proportional Intensity NHPP is to test delta == 1. And the test for Loglear NHPP is to test delta == 0. If you put these numbers back into the formula, you should see time disappear from the formulas.

HPP is a simpler model than NHPP's. If tests cannot reject HPP, one may prefer using HPP for further decision making.

If the process is indeed HPP, the inter-arrival times are iid Exponential distributed. But one should not analyze inter-arrival times as iid to determine whether a process is HPP.

[#3]

Ok! roger that! many many thanks!!