Fill in the blank. The distribution is a discrete probability distribution that applies to the number of occurrences of some event over a specified interval. The distribution is a discrete probability distribution that applies to the number of occurrences of some event over a specified interval.

Step 1 ：The question is asking for the name of a discrete probability distribution that is used to model the number of occurrences of an event in a specified interval. This is a definition of the Poisson distribution.

Step 2 ：Final Answer: The distribution is a \(\boxed{\text{Poisson}}\) discrete probability distribution that applies to the number of occurrences of some event over a specified interval.