Parametric test if underlying assumption is gamma distribution I'm trying to concudt an A/B test where I want to compare the mean of two groups of customer spendings and decide whether they are significant or not. I have a dataset of 10 000 customers and their total spendings within a period of time, however around 8500 of these are zero. So the histogram looks like this for the raw data:

Where the x-axis is the customer spending. A quick instinct was to remove the 0 frequencies and the rightmost outliers, then I got this

where i've fitted a gamma distribution with parameters $a=1.909$ and $b=662.039$.
Questions:

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*It seems wrong to just remove the 0 at the start since the number of customers that don't purchase (i.e don't respond to a campaign or e-mail) is important to distinguish between the groups.

*Assuming that the first point above is somehow OK to do, then I can assume gamma distribution and in that case, what statistical test can I apply to do the test?

*Would it maybe be better to do a non-parametric test instead?


Take a look at "A Deep Probabilistic Model for Customer Lifetime Value Prediction" which provides a training algorithm to learn CLV from high dimensional feature spaces using zero-inflated log-normals (ZILN).  Changing this to a zero-inflated Gamma distribution is a trivial exercise.
In particular, they explain why looking at mean squared error (and hence means) is a sub-optimal way to look at this type of problem, because it a) does not work well with the high number of zeros; and b) ignores the right skew in the data.
I would suggest to look at the underlying business problem again and see if a quantile based comparison is more relevant for decision makers. I suspect that decision makers will care about two things: churn rate and long term life time value for returning customers.  The ZILN model allows you to estimate both (and get confidence [or posterior] intervals for both).
Last but not least, if you still want mean comparisons, then you can always compute the mean of the zero inflated log normal based on parameter estimates.
