I have data of sales per day during a certain period (n=7939). The data is rather skewed (see the first image below). I would like to propose the number of items to resupply every day such that for 95% of the days there is enough stock. It is given that the stock is resupplied every day and a big surplus of stock is considered waste. We can disregard seasonal influences.
Since I want to consider the number of items that would satisfiy 95% of the days, I simply took the 95th percentile of the sales. However, taking this percentile gives us no idea of the confidence interval. I felt there must be a more solid approach.
To resolve this, I applied bootstrap resampling and computed the 95th percentile of each sample. I performed this operation a thousand times. The idea is to make use of the central limit theorem. With normally distributed sample percentiles I can provide the mean and the 0.025 and 0.975 percentile of the sample percentiles as confidence interval.
However, the problem is that my data is very "binned" and I don't know where to go from here.
Basically I have two questions:
- Given my problem, is this a valid approach? Is there a different approach that might be more suitable for this problem?
- Is the binned distribution a problem for assuming normality (and thus provide the confidence around the mean 95th percentile).