I am trying to find out if there's a standard name for the following distribution related to the binomial distribution. This distribution is basically the same as the binomial distribution, but as if the second half of the probability mass function (PMF) is flipped and added to the first half.
I am assuming the binomial distribution's PMF is given by:
$$f(k) = \left( \begin{matrix} n \\ k \end{matrix} \right) p^k q^{n-k}$$
where $q=1-p$, and $k \in \{0, 1, ..., n\}$.
The PMF of the distribution I am looking for the name of is then given by:
$$g(k) = f(k) + f(n-k)$$
when $n$ is odd, $k \in \{0, 1, ..., (n-1)/2\}$
and for $n$ even:
$$g(k) = \begin{cases} f(k) + f(n-k) & k<n/2 \\ f(n/2) & k=n/2 \end{cases}$$
where $k \in \{0, 1, ..., n/2\}$.
