# What is Poisson density multiplied by integer-Gaussian?

What is Poisson density multiplied by integer-Guassian?

$$p(X=x)\propto\frac{\theta^x}{x!}\exp(-x^2),\quad x\in\mathbb{N}$$

Is it a distribution being studied?

• It's also unclear what you seek when you say "what is...". Assuming you can resolve Artem's question, what is it you want to know about the resulting pmf? Are you seeking a name for it, or some property of it? Apr 1 '19 at 22:19
• I don't see how "Poisson multiplied by Gaussian" describes this pdf. It's identical to the Poisson pdf except that it uses exp(-x^2) instead of exp(-x). I've never heard of any use for that distribution. Apr 2 '19 at 3:52
• @HeleneHoegsbroThygesen Poisson is $\exp\left(-\theta\right)$
– ZHU
Apr 2 '19 at 4:27
• oh yes of course, thanks! Apr 2 '19 at 21:53