# Confidence in Negative Binomial Prediction

I have predicted future demand of stock from observed historical demand projecting a negative binomial demand curve. Demand is extrapolated to multiple periods using this approach.

I'm pretty happy with the demand curve this is generating but I have concerns over the confidence levels of the mean and variance parameters I'm supplying to the model which are generated by observation of historical demand.

I see there being some unknown variability around the observed historical sample mean ie if the historical period is offset by 6 months or 1 month or whatever, the mean being given to the model will be different.

In an attempt to account for this uncertainty I wanted to generate a confidence interval around the sample mean. Because the Negative Binomial curve does not conform to a normal distribution, I used central limit theorem to capture the mean of means and used this normal curve to get 95% confidence in the mean. I then fed the the mean of the means and the upper confidence mean as parameters into two separate negative binomials. The difference between the two outputs allowed me to give a confidence band as in the 2nd of 2 charts below shows.

The key issue is that i'm not clear whether I need to do this Central Limit step at all or whether the original demand curve i'm generating accounts for uncertainty in the mean (and variance) parameters I am feeding it already. So in a nut shell is chart 1 or chart 2 the final step?

(Not a stats guy and quite confused)

Service demand curves using only observed mean demand

Service demand using Central Limit mean of means and 95% mean