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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?

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  • $\begingroup$ If your probability is « front-loaded » as you say, you could use a Geometric distribution to count the number of days before the event happens. $\endgroup$ – Maximilian Aigner Aug 26 at 19:04
  • $\begingroup$ There isn't enough information here to determine whether any of the infinitely many possible answers is any good. Could you provide some more specific--preferably quantifiable--characterizations of the desired properties of this distribution? What theories or data do you have that can inform this choice? $\endgroup$ – whuber Aug 26 at 21:47