Find the best distribution

Posted on 2013-12-04
Last Modified: 2013-12-14
Hi experts,

I have a data which represent the request comes into development center. I need to know the distribution of the arrival data into that center. I have calculate the inter-arrival time and calculate the frequency of the inter-arrival time. So, how can I know the fit probability distribution for this data?

* Please find a sample of the data file (an example)
Question by:amq10
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LVL 37

Assisted Solution

TommySzalapski earned 167 total points
ID: 39696821
The most common way I see that type of problem represented is the Poisson distribution. You could start there.

Of course, in reality, the time of day or day of the week can have a pretty big impact on the number of requests so it depends on how sophisticated of a model you want.
LVL 27

Assisted Solution

d-glitch earned 333 total points
ID: 39696842
If you fix up your data so it is all in date format, you change it to integers to see the Julian day number.

Then you can find the interarrival times and find the average.

I don't know if this could be modeled as a Poisson process or not.
LVL 27

Assisted Solution

d-glitch earned 333 total points
ID: 39696870
Issue Type	CREATED				
New Feature	11/10/2011     	40857			
New Feature	2/1/2012	40940	83		
New Feature	4/11/2012	41010	70		
New Feature	4/14/2012	41013	3		
New Feature	5/2/2012	41031	18		
New Feature	7/10/2012	41100	69		
New Feature	7/31/2012	41121	21		
			264	 / 6  ==>	44.00

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LVL 27

Assisted Solution

d-glitch earned 333 total points
ID: 39696875
The inter arrival times vary between 3 and 83 days.
Is there any reason to think this is a random process?
LVL 84

Expert Comment

ID: 39696894
7 data points are not enough to determine a model much more sophisticated than Poisson.
It's easy enough to find more complicated models that fit the data, but you'd probably just be fitting idiosyncrasies in the particular data set in a way that won't generalize to any other data.

Author Comment

ID: 39696999
Thanks for all,

Actually, it is a real data and more than 2000 record. I have calculate the inter arrival time and calculate the frequency to plot it and see which distribution can use. I have attached what I have got from plotting the frequency . The problem is I have problem to scale the data. SO, I plot it in minutes as shown in attached file.
LVL 37

Assisted Solution

TommySzalapski earned 167 total points
ID: 39697008
Try fitting it to a Poisson model and see if that gives you what you need. That's really the go-to distribution for random arrival.

Author Comment

ID: 39712433

Still stuck with this problem. I have no idea where is the problem. to simplify the problem,  I have the attached data as a time of arrival tasks to a center, I need to find the fit distribution to set the simulation. So, I calculate the inter-arrival time between coming tasks and try to plot the frequency in histogram to compare it with Poisson distribution.

The question is that: does my steps correct to find the fitness distribution for my arrival point?

How can I calculate the Poisson distribution for this data or how to find the best distribution?
LVL 27

Accepted Solution

d-glitch earned 333 total points
ID: 39714623
You need to cleanup your data.  

Are all of your data in the same date/time format?  It doesn't appear to be.

Most of the interarrival times are less than 1.00, but then there are runs of integers and zeros.
What does a zero value mean?  Do you have multiple events happening at the exact same time?

Looking at the data by eye:
   The events/day for the first seven days are 20, 12, 25, 31, 11, 32, 24.
   This is great.  It is analyzable.  You might even be able to model it as a Poisson process.

But then you have a twenty day gap from JAN-11 thru FEB-2.  
What is going on?  Do you understand why this gap occurs?
You have a number of these gaps in your data.
What do you hope to learn from your analysis?

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