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Normal distribution vs.exponential

  1. Apr 16, 2012 #1
    Sorry because I have asked this other times but still not getting a reasonable answer:

    For bus headway times why in several articles they make assumption of normal distribution??
    Generally inter-arrival times are modeled using exponential distribution but in some papers
    http://onlinelibrary.wiley.com/doi/10.1002/atr.5670250304/abstract
    http://www.sciencedirect.com/science/article/pii/0191261586900366

    normal distribution is assumed.
    Which are the reasons to make this assumption?
    Maybe because the real time is calculated including time for passengers to enter in bus and departing?
    Maybe because of normal distribution quality of modeling deviations from some point (scheduled time) ?

    Please help
    Regards
     
  2. jcsd
  3. Apr 16, 2012 #2
    Exponential distributions are a family of distributions that include the normal distribution. Generally, whenever something can be modelled by an exponential distribution and there is no addition information to clearly specify which specific exponential distribution is to be used, a normal distribution will be assumed for various reasons that include the central limit theorem and some basic results from information theory (the normal distribution has the greatest amount of "uncertainty" associated with it out of all exponential distributions, and so, in a sense, it makes fewer assumptions than the others).
     
  4. Apr 17, 2012 #3
    Yes but it is rather vague.
    I was thinking if travel time = bus headway + time spent at the stop then if bus headways for example are exponential and time spent at the stop some other distribution than I gues their sum is not exponential but someway renewal process so maybe there will be some approximation to normal?
     
  5. Apr 17, 2012 #4

    Office_Shredder

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    Number nine, the normal distribution is not an example of an exponential distribution.

    Mark, reading the second paper (pdf found here http://www-bcf.usc.edu/~maged/publications/Optimal Holding Times.pdf ) I see that the amount by which a bus is late is modeled as a normal distribution, but I don't see where they talk about the amount of time between buses being a normal distribution (which doesn't really make sense because the distribution should have only non-negative numbers as its support)
     
  6. Apr 17, 2012 #5
    Office Shredder you are totally right.
    Anyway is there any orientation about normal assumption in bus travel time modeling you can give please?
    Best regards
     
  7. Apr 17, 2012 #6
    I interpreted the OP (perhaps incorrectly) as being about something from the exponential family of distributions, of which the normal distribution is a member. In retrospect, that's almost certainly not what he's talking about.
     
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