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
Carlo Beenakker
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