Does anybody know the name of the discrete distribution with these properties? I'm looking for a distribution which has the following properties.  I don't know what it's called so I'm having a hard time finding references to it.
Properties:


*

*Domain is over a finite range of integers (distribution is discrete and truncated)

*Range is over the reals

*The sum over the distribution is equal to 1

*The first and second moments (mean and variance) are defined and are independent of one another

*The entropy of the distribution is maximized given the above constraints.


A normal distribution would fit these criteria if the domain was over all of the reals.  Likewise, a truncated normal distribution would fit if the domain were in a range of reals.
The binomial distribution can't be right because there's only one free parameter p which affects both the mean and variance.  Likewise the hyper-geometric distribution doesn't fit either.
Does anybody know if this distribution has a name?

The solution is again a discrete, truncated Gaussian. With Lagrange multipliers, the objective function is
$$
\sum_n p_n\log p_n+\lambda\sum_np_n+\mu\sum_nnp_n+\nu\sum_nn^2p_n\;.
$$
Setting the derivative with respect to $p_i$ to zero yields
$$
\log p_i+1+\lambda+\mu i+\nu i^2=0\;,
$$
which yields a Gaussian, with the three Lagrange multipliers determined by the three (transcendental) conditions given by the normalization, mean and variance.
