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 <A HREF="http://www.worldresearchlibrary.org/up_proc/pdf/1124-15114160424-7.pdf">The derivation of diffusion-jump modes for power plant projects under risk</A>. A more correct terminology would be to call $\Phi$ the *complement of the binomial cumulative distribution* function, which is how it is called in <A HREF="https://www.mathworks.com/help/stats/binocdf.html#mw_d8519302-0c92-417f-88f9-a27b6a3f4e7f">MatLab.</A>