Let's say I have a 30-day period in which one specific event can only occur, at most, once. The probability of the event happening on Day X is likely to be front-loaded (eg. the event is more likely to happen on Day 1 than Day 2, more likely on Day 2 than Day 3, etc.).
My thinking is that this is best captured with a binomial distribution, with the probability of the event happening changing from day to day, since that allows for the possibility that the event doesn't happen at all. Is there another distribution that better captures this?