Is sum of two negative binomial variables also distributed as negative binomial if they are non-idependent and correlation is $ < 1$? Or not?
2026-02-23 22:23:38.1771885418
Distribution of sum of correlated negative binomials
89 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
No. For instance if $X$ and $Y$ are independent negative binomials and $Z = X+Y$ (which is negative binomial and has correlation $<1$ with both $X$ and $Y$) then $X+Z=2X + Y$ is not negative binomial. (I'll leave the proof up to you since you changed the question on me.)