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How to plot the graph of my data to compare it with Poisson graph?

Posted on 2013-12-14
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Last Modified: 2013-12-29
Hi,

I have the following format of the arrival data to center. I need to plot the frequency graph to compare it with the Poisson graph which I have done it. What is the graph should I plot to compare it with the Poisson distribution? and how can I do that?

*the tasks to the center more than 3000 but I have put below an example.

04/03/2013 13:41
04/03/2013 13:49
04/03/2013 13:50
04/03/2013 13:53
04/03/2013 14:02
04/03/2013 14:07
04/03/2013 14:10
04/03/2013 14:18
04/03/2013 14:27
04/03/2013 14:31
04/03/2013 14:52
04/03/2013 14:52
04/03/2013 15:06
06/03/2013 08:43
06/03/2013 09:20
06/03/2013 09:32
06/03/2013 09:52
06/03/2013 09:56
06/03/2013 10:30
06/03/2013 10:58
06/03/2013 11:09
06/03/2013 11:17
06/03/2013 11:21
06/03/2013 11:32
06/03/2013 11:55
06/03/2013 12:03
06/03/2013 12:10
06/03/2013 12:19
06/03/2013 12:24
06/03/2013 12:26
06/03/2013 12:39
06/03/2013 12:45
06/03/2013 12:46
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Question by:amq10
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LVL 27

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d-glitch earned 500 total points
ID: 39723957
I assume you have access to Excel.

1.  Put an event counter in the first column.
2.  Put your data in the second column.
3.  Calculate the interarrival times in the third column.
4.  Use Copy and Paste Special Values to copy the IntArr values in a new columm.
5.  Sort this column in descending order.
6.  Calculate the Average Interarrival Time for your data.
7.  Generate an Ideal Poisson distribution based on the measured average.
8.  Plot the Sorted and Ideal distributions on a log-log scatter plot.

You should get a straight line, as in the attached example.
Poisson-for-ExEx.pdf
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LVL 27

Assisted Solution

by:d-glitch
d-glitch earned 500 total points
ID: 39724401
Some notes on my example:

[C3] is set to Time=0

The formula I used to generate the Time for Event_1 is     [C4] = C3-LN(RAND())/10
You can drag this down to generate as many events as you want.

The 10 in the denominator should yield 10 events/day on average.  
The actual value in the Example was     30 events/3.4046 days  =  8.82 events/day

The interarrival times are the differences between successive events.

The average interarrival time is     1/8.82  =  0.1135 days

The formula I used to generate the Ideal Poisson distribution is [G4] = -LN((A4)/30.1)*F$35.
     A4 <= Event Number        F$35 <= AvgIntArr
You can drag this down to match the number of events.

There are 30 events, but I used 30.1 in the formula to avoid a problem with lower endpoint of the range.   LN(1) would give a IntArrTime of zero.
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