# Parameterization with truncated normals

We want to model \beta \sim \text{Normal}^+(\mu,\sigma), a Normal distribution truncated below at 0, where \mu and \sigma are fixed (and do not depend on parameters). Is the below what you recommend? So that things in the parameters block have unit scale?

parameters {
real<lower=-mu/sigma> beta_raw;
}
transformed parameters {
real<lower=0> beta;
beta = beta_raw * sigma + mu; // want ~ N^+(mu,sigma)
}
model {
beta_raw ~ normal(0, 1);
}

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That is fine if mu and sigma are in (transformed) data.

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