# Is there a closed-form maximum-entropy analogue of the exponential distribution, but restricted to integers?

I've used exponential distributions to estimate maximum-entropy probability distributions before.

Is there an analogue to the exponential that is restricted to integers? If so, does anyone have pointers to closed-form estimators for that distribution?

The discrete equivalent of the exponential distribution is the geometric distribution.

Wikipedia gives this as the maximum-entropy distribution under certain assumptions