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I'm trying to run a Monte Carlo to determine a set of given weights.

I have 5 weights (w1 to w5) that add up to 100%. Many people have different opinions on what these weights should be. We have collected 40-50 samples of what people view the weights as being. For example:

Person 1: .40 | .30 | .10 | .10 | .10

Person 2: .30 | .20 | .20 | .10 | .20

Person 3: .40 | .25 | .15 | .15 | .15

etc.

I want to run a Monte Carlo by using the data points we've collected and creating a distribution for each weight. Then I will randomly draw a from each distribution over many iterations.

Is this the correct approach?

Additionally, what distribution should I use to model these weights? Two constraints I see:

  • no weight can be less than 0
  • all weights must add up to 1.0

Any advice or assistance is much appreciated.

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Perhaps you should have a look at bootstrapping methods. –  Libra Mar 21 '13 at 18:15

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