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Adding Poisson Noise

Posted on 2003-03-10
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Last Modified: 2012-05-04
Hello,

The problem that I have is that I am trying to add Poisson distributed noise to a set of data, which is simply stored as a list of numbers. I was wondering if anyone knew any easy ways of performing this task.

Many thanks

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Question by:FaustVs
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Expert Comment

by:tilex
ID: 8104116
Can you explain more what you want? I don't understand your question, what is Poison Nose?
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msa2003 earned 200 total points
ID: 8104495
Poisson distribution looks like:

P(X = m) = (a^m)*exp(-a)/(m!)
where a=M(X)

First, choose a range of X Poisson-distributed values. Because X allwais is a integer number, the range will contain a number of possible values. For example, if a=0.1 there is enough to calculate 5 values (X = 0 ... 4); if a=10, 30 values is enough. Probabilities of the other values will be very small (less then 0.000001). Build the table of (X, Y) values using the following rules.

   P(0) = exp(-a);
   P(X + 1) = P(X) * a / (X + 1);
   Y(0) = P(0);
   Y(X + 1) = Y(X) + P(X + 1)

Now suppose that we have random generator with uniform distribution (for example, pascal's Random function) which will generate continuous values from 0 to 1 exclusively. Call it R. Generate R = 0 ... 1 and using binary or straight search find the nearest Y(X) value. X will be the poisson-distributed value.

This method is called "table method" and could be used to generate a number X values with constant a (Poisson distributed noise).
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by:msa2003
ID: 8104510
tilex: learn math ;)
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Expert Comment

by:tilex
ID: 8104576
I'm only in secondary 3...I don't konw what's its like in US but well I'm 15, IV'E got math notions but I'm not that far...
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Expert Comment

by:msa2003
ID: 8105925
tilex: I hope you would like it ;)
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