Hi everyone!

I have a more general question:

Are there any specific customs or guidelines on how to reparameterize the distributions we use for **positive** parameters? I have a model with a number of (weakly) positive parameters and so far fared well with the approach discussed here, i.e., just drawing from a Normal distribution and restricting the parameter to be positive.

However, I got some divergences in my models and may want to re-parameterize, but I’m unsure how to proceed. Of course, the normal distribution can be easily re-parameterized (see below), but how would you go about ensuring it remains positive? Restricting the “raw” z-score doesn’t make any sense to me and simply restricting the final parameter lead to STAN complaining that parameters are outside their legal range (which makes sense to me).

```
parameters {
real p_mu;
real p_sigma;
real <lower=0>param;
real p_raw;
}
model {
param ~ normal(p_mu,p_sigma);
...
//reparameterized version:
param_raw ~ std_normal()
param = p_mu + param_raw*p_sigma
}
```

This got me thinking that it’s **probably better to use a different distribution anyways**. The exponential distribution seems like it can be easily reparameterized (as discussed here) , but is this really my only option?

```
//reparameterized exponential
parameters{
real p_rate;
real param_raw;
real param;
}
model{
param_raw ~exponential(1)
param = 1/p_rate * param_raw
}
```

To sum up, I have two questions:

- Am I right in abandoning the reparameterized half-normal for positive parameters?
- What other distributions are appropriate, and how can I reparameterize these distributions?

Thank you for your guidance!

Best

N