There are five different periods (one following each other) of unequal lengths where one specific event is happening such that it follows Poisson distributions (e.g. meteorite falls). It is always the same type of event, just the expected average time between event is changing from time to time. In reality there are many more such periods.

The data look like this:

 - in the 1st period (100 hours) the average interval for event is 500 hours 
 - in the 2nd period ( 80 hours) the average interval for event is 700 hours
 - in the 3rd period (130 hours) the average interval for event is 300 hours 
 - in the 4th period ( 50 hours) the average interval for event is 800 hours 
 - in the 5th period (400 hours) the average interval for event is 900 hours

Lambda:
 - 1st period lambda: (1/500)*100 = 0.200
 - 2nd period lambda: (1/700)*80  = 0.114
 - 3rd period lambda: (1/300)*130 = 0.433
 - 4th period lambda: (1/800)*50  = 0.062
 - 5th period lambda: (1/900)*400 = 0.444

Is there a way to estimate how many events happened and what is the confidence interval for the estimate?

I understood from https://stats.stackexchange.com/questions/15371/how-to-calculate-a-confidence-level-for-a-poisson-distribution and here: http://ms.mcmaster.ca/peter/s743/poissonalpha.html that I can use (x is number of events):

 - ( qchisq(0.025, 2*x)/2, qchisq(0.975, 2*(x+1))/2 )

or maybe some other method that will be more suitable for low lambda.

I don't understand how I can add all the five distributions together to say how many events were expected.