# What are some common approaches for estimating variability of right skewed, bimodal distributions?

I have a data set with the dollars in transactions a store has done historically from noon-2pm on Wednesdays. Most of the time, the store does no volume during this time (16 observations with the value of 0), but when it does one or more transactions, since the minimum price for an item is around 400, those observations occupy a second mode around $800. What are some approaches one might take to estimate normal variability in such a situation with an eye towards using that approach for detecting outliers? For the domain context, given this store's volume, I would roughly consider anything below$1700 normal variation, anything above 3000 as a significant outlier, and anything in between slightly anomalous, but not full fledged outliers. I'd like to find an approach that would allow me to accurately represent normal variability and outliers for a wide range of store sizes and activity levels that fundamentally follow a similar distribution.

I've tried using the standard deviation, but this doesn't seem to capture what I'd like to consider normal deviations vs. outlying deviations. For example, I would want to represent values close to the right hand mode as normal deviations from the mean, but the point estimates for mean and standard deviation return z-scores that are > 1 for new observations that fall around the right mode.

One approach I considered was just to use the non-zero right mode values to calculate the mean and standard deviation to calculate z-scores from, but that has the disadvantage of not incorporating information from the left side of the distribution. For example, for samples with relatively more 0 value observations, the probability of experiencing an extreme value should be lower than for a sample with relatively fewer 0 value periods.

My ultimate desire is to be able to observe new values in subsequent Wednesday noon-2pm periods and determine whether that new observation falls within what could be considered normal population variation vs. is an outlier.

Any suggestions are greatly appreciated!