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Normal distribution vs.Exponential distribution

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In many books interarrival times between 2 successive bus arrivals are modeled by using exponential distribution.

Anyway there are a lot of papers where this time is referred as bus travel time = bus headways + time spent at the bus stop (time for passengers to enter in or go out)

This travel time is modeled as normal distribution.

Are there any reasons (theoritical) to use this distribution rather than exponential or others?

I need some arguments without entering in normality tests or 3sigma proof.

Please help

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Waiting time between successive events might be exponential, but this Bus Travel Time (which is the sum of an exponential and another rv) might be normal. Some background might help you get this question answered.

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