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I'm trying to think of a distribution to model the following situation.

People enter a market having different beliefs. Two non-negative integers can represent the belief $G \in \{0,1,....\}$ and $B \in \{0,1,...\}$, the number of good and bad experiences in the past. Two experiences are assumed to be independent and exogenously given.

I need an excellent way to represent this combination of $(G,B)$ with a probability mass function that goes to zero if one of the numbers goes to infinity (or any other way to handle an extreme case).

Any suggestions would be greatly helpful!

I decided to stick with a binomial distribution where $Binomial(k,n,p)$ where $k$ is the number of $G$, $n$ the number of past visited occasions, which I should assume every potential customer has the same $n$, and $p$ to be the probability of a past visit being a good experience. I'm not sure if there is a better distribution than this.

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  • What is the tag distribution-theory about? – md2perpe Mar 23 '23 at 21:24
  • I removed it, I suppose he didn't know that distribution theory is not for probability distribution – LL 3.14 Mar 23 '23 at 22:14
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    Wikipedia has page for list of probability distributions, discrete ones, with infinite support. E.g., Poisson. Making each $G$ and $B$ Poisson, given you want them to be independent, their joint is just a product of the marginals. – Jan Mar 23 '23 at 23:59

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I decided to stick with a binomial distribution where (,,) where is the number of , the number of past visited occasions, which I should assume every potential customer has the same , and to be the probability of a past visit being a good experience. I'm not sure if there is a better distribution than this

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