Assumptions about arrival independence

[Mark J.]

Hi

How to be mathematically correct about assumption of independence about arrivals of clients at a bank?
Physically I understand that there is no possible dependence between2 sequent arrivals of clients but anyway when I make this assumption I want to be correct according literature.

Maybe some arguments or linking to some literature?

Regards

 

[mathman]

The assumption of independent arrival is a given for doing the math. Whether it is true or not depends entirely on the physics.

Once you make the assumption (independence), as your question states, then you can do the math using the assumption.

 

[Mark J.]

My case is clients arriving in bank and I have to explain why I chose Poisson to model this process before entering in data analysis.
Can you give me any explanation on this?
Regards

 

[haruspex]

As mathman said, there is no mathematical justification for assuming the arrivals to be independent. The only way to justify it is by consideration of the real world process being modeled. In fact, there are lots of good reasons why they would not be! Many go to the bank in their lunch breaks, and these tend to be synchronised. Some will arrive before the bank opens, creating an initial rush. Others have more flexibility and will pick times when they expect the queue to be short. Weather also creates bunching...
There will be ways of analysing the data to determine how closely it fits Poisson, but that was not your question.

 

[Stephen Tashi]

I have to explain why I chose Poisson to model this process before entering in data analysis.

To imagine that your question has an answer, I must pretend that these are directions for an assignment in a course and not a real world problem. Thinking about it that way, you could say that we imagine a time interval to be divided up into man small bins of, say, 0.1 second duration. Relative to the numberof bins, there are few people arriving and thus a neglible probability of two people arriving simultaneously. A person who intends to arrive at time t will be affected by many independent events that hasten or delay him, so the probability of his actual arrival time is spread out over a time interval.

Such a problem is a typical exercise in mind-reading what an instructor wants you to say. It doesn't have a standard mathematical answer. Your text or instructor probably told you about the assumptions that imply a Poission process. Just go through that list of assumptions and demonstrate that you thought about whether the assumptions hold (approximately) in the case of bank customer arrivals.