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Given to integers $n < m \in \mathbb{N}_0$ and a probability $p$, I'm struggling to calculate (or at least get an upper bound for) the quotient $$Q = \frac{F(n+1;m,p)}{F(n;m,p)}$$ where $F$ denotes the cumulative binomial distribution function, i.e. $$F(n;m,p) = \sum_{k=0}^n \binom{n}{k} p^k (1-p)^{n-k} \text{.}$$$$F(n;m,p) = \sum_{k=0}^n \binom{m}{k} p^k (1-p)^{m-k} \text{.}$$ Any help would be really appreciated, thanks!

Given to integers $n < m \in \mathbb{N}_0$ and a probability $p$, I'm struggling to calculate (or at least get an upper bound for) the quotient $$Q = \frac{F(n+1;m,p)}{F(n;m,p)}$$ where $F$ denotes the cumulative binomial distribution function, i.e. $$F(n;m,p) = \sum_{k=0}^n \binom{n}{k} p^k (1-p)^{n-k} \text{.}$$ Any help would be really appreciated, thanks!

Given to integers $n < m \in \mathbb{N}_0$ and a probability $p$, I'm struggling to calculate (or at least get an upper bound for) the quotient $$Q = \frac{F(n+1;m,p)}{F(n;m,p)}$$ where $F$ denotes the cumulative binomial distribution function, i.e. $$F(n;m,p) = \sum_{k=0}^n \binom{m}{k} p^k (1-p)^{m-k} \text{.}$$ Any help would be really appreciated, thanks!

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Permutant
Permutant
  • 11
  • 3

Quotient of cumulative binomial distribution functions

Given to integers $n < m \in \mathbb{N}_0$ and a probability $p$, I'm struggling to calculate (or at least get an upper bound for) the quotient $$Q = \frac{F(n+1;m,p)}{F(n;m,p)}$$ where $F$ denotes the cumulative binomial distribution function, i.e. $$F(n;m,p) = \sum_{k=0}^n \binom{n}{k} p^k (1-p)^{n-k} \text{.}$$ Any help would be really appreciated, thanks!