Just what the title says. I want to model probability of number of sales on a given day. I can't use poisson/binomial, because there are indications that the standard deviation of the sales might differ between two products with the same average number of sales.
Is there a discrete version of normal distribution, or something like poisson distribution in which you can independently set the variance?
For count data like you describe, you probably want a negative-binomial distribution. This is an extension of the Poisson distribution that has an additional parameter that allows for the variance not to be tied to the mean. This is a distribution that is commonly used for count data, either for straight count data, or in problems where you also have other explanatory variables (where you can use a negative-binomial GLM). There are some other statistical models that are used for count data, but that is where I would start. You needn't worry about the connection to the normal distribution here; just look for a distribution that is appropriate to your count data.
