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The complementary binomial distribution is defined by $$\Phi(a;n,p)=\sum _{j=a}^n \binom{n}{j} p^j(1-p)^{n-j},\;\;0<p<1,\;\;0\leq a\leq n.$$ see The derivation of diffusion-jump modes for power plant projects under risk. A more correct terminology would be to call $\Phi$ the complement of the binomial cumulative distribution function, which is how it is called in MatLab.