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I would like to run a monte carlo simulation for a financial model what needs to predict sales. I have somewhat successfully done this if I assume the average order size is normally distributed (at say 80) and has a standard deviation (of say 30). However, the problem is that the minimum sale of course can't be less than 0. Can someone suggest a good alternative distribution (or technique for working with a normal distribution) to handle this problem (I am sure it must be a common enough scenario!). Thanks.

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Sales are often assumed to be Poisson distributed, based on the Poisson's properties of modeling "the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event", to quote from Wikipedia - which one could argue applies to people buying stuff.

A little more thinking leads us to think about pantry loading, stocking up or hoarding, which would lead to overdispersed data, which can be modeled using the negative binomial distribution.

However, sales are often also seasonal or driven by promotions and/or price changes, so you should really think about including such factors in your model, which is when you will end up with the regression variants of the above, i.e., Poisson regression or negative binomial regression.

And you are right in that this is a common scenario. People make their living doing this. Like yours truly ;-)

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  • $\begingroup$ Thanks Stephan....I see from your profile you are definitely the man to answer this question! I will experiment with all of the above. $\endgroup$ – Mike Hanrahan Feb 13 '13 at 18:13

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