Generalized distribution time series moving averages

I'm trying to figure out a pattern that I'm seeing. I have weights generated by an unknown function F

F(3) = [-3/9, 2/9, 6/9, 3/9, 1/9]
F(4) = [-8/16, -1/16, 5/16, 10/16, 6/17, 3/16, 1/16]
F(5) = [-15/25, -6/25, 2/25, 9/25, 15/25, 10/25, 6/25, 3/25, 1/25]
...


I understand how the function is generating the series/weights, but I'm wondering if there's any more nuance or theory behind the weight generation. I know that that weights are generated according to some time series manipulation (likely manipulations of moving averages of different lengths). Curious if anyone has seen anything like this and could enlighten me on the theory behind these weights

• Probability distribution with negative values? How could this work? How does it work in your specific case? Commented Jun 16, 2017 at 12:02
• I am afraid you must tell us more on what F is and how were the weights generated and what is the generalized probability distribution that you are talking about. I agree with @KarelMacek that this doesn't make much sense at first sight (how would you define negative probability?).
– Tim
Commented Jun 16, 2017 at 12:14