Normal distribution vs.exponential...


by Mark J.
Tags: distribution, normal, vsexponential
Mark J.
Mark J. is offline
#1
Apr16-12, 03:01 PM
P: 77
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/1...50304/abstract
http://www.sciencedirect.com/science...91261586900366

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
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
Number Nine
Number Nine is offline
#2
Apr16-12, 03:40 PM
P: 771
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).
Mark J.
Mark J. is offline
#3
Apr17-12, 11:12 AM
P: 77
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?

Office_Shredder
Office_Shredder is offline
#4
Apr17-12, 02:18 PM
Mentor
P: 4,499

Normal distribution vs.exponential...


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/public...ng%20Times.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)
Mark J.
Mark J. is offline
#5
Apr17-12, 02:38 PM
P: 77
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
Number Nine
Number Nine is offline
#6
Apr17-12, 03:05 PM
P: 771
Number nine, the normal distribution is not an example of an exponential distribution.
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.


Register to reply

Related Discussions
normal and exponential-normal (?) distribution Calculus 0
Comparing normal distribution divided by normal distribution Set Theory, Logic, Probability, Statistics 12
Is 2 times normal distribution still a normal distribution please? Set Theory, Logic, Probability, Statistics 4
Confidence Intervals: t-distribution or normal distribution? Set Theory, Logic, Probability, Statistics 4
Exponential growth and exponential distribution Set Theory, Logic, Probability, Statistics 3