Estimating the Binomial Tail

We saw in the previous chapter that the Helmholtz principle in his generic form leads us to the computation of the probability of events of the type “at least k objects out of l have a considered quality”. When the a-contrario assumption is that objects are independent and have the same probability p to have the quality, the probability of this event is given by the binomial distribution. In this chapter, we will give different inequalities and asymptotic results for the binomial tail. Such results are useful mainly because they help us to understand the “meaningfulness” of an event as a function of l, k, and p. The results given in this chapter will be used through the rest of the book.