I have two data sets

1. Age of all the surviving firms at any given point of time. The age distribution is an exponential function

2. The age of all the firms which died at a given point of time ( In this case, the firms not submitting mandatory annual reports were given a notice and declared closed.). The age distribution is also an exponential function.

Both the datasets are substantially large.

My question is

How can I calculate a relationship between the two exponential functions? What should be the approach. We should have firm specific data to relate the survival function and hazard function. But in this case the data is not firm specific.

Any lead to the problem is sincerely appreciated.

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