Thanks Daniele for the edits.

Hi, "Φ(a;n,p) is the probability that the binomial random variable takes a value in the range a,a+1,…n", it means it's complementary probability distribution function as per the MatLab site you posted right?

p′ = (u/r)p and 1 – p′ = (d/r)(1 – p)

Hi, thanks for the answer. I will checked it, but it contains same step like the paper I mentioned and I am trying to understand that only. What exactly is complementary binomial distribution function and how this is derived:

Hi, the format of expression is not getting pasted properly. I tried attaching image of it also, but it says I don't have sufficient reputation points. Can you please suggest an alternative.