Hi,

I wanted to ask for some input on my choice of likelihoods for different models I am building. Also, I’ll be using brms and some of the options I found through Wikipedia are not listed in the brms family list so maybe I’d go with the ones that are?

### 1.

The outcome is a positive integer representing the number of positive cases in the first n positions of a ranked list. I also know the total number of positive cases, although they can differ between samples.

I would probably model this with a Poisson distribution, although the hypergeometric, binomial and negative-binomial distributions also sound like possible candidates.

**Edit:** Turns out I don’t know the maximum number of positive cases, so probably just a poisson?

### 2.

The outcome represents the area under a curve and lies between but not including 0 and 1. I am pretty sure I will model this with a beta distribution.

#### 2.1

I also have cases, where I only look at the first part of the curve, so that the areas lie between eg. 0 and 0.05 but in some cases, this can be 0.

Here I don’t know how to model it as I can’t just scale it to 0-1 and use a beta again due to the 0’s.

Would a transformation like exp(var)/e be viable to scale it to 0-1 and use a beta or is there a better solution?

I thought about a zero-inflated beta, but am not sure what to use to model the zi term.

### 3.

Final outcome is a run-time, so a positive float. I was thinking about a truncated normal, exponential or lognormal but don’t really have arguments for or against any of these due to lack of experience.

Thank you for any help in advance :)