Skellam distribution

Modeling
1

Is the Skellam distribution available via APIs? If not, any workaround?

2

In what software are you referring?

In Stan, you can just code your own probability distributions in the function block from the math on wikipedia; something like, e.g.,

functions {
  
real skellam_lpmf(int k, real lambda1, real lambda2) {
  real r = k;
  return -( lambda1 + lambda2 ) + (r/2) * log( lambda1 / lambda2 ) 
         + log( modified_bessel_first_kind(k, 2 * sqrt(lambda1 * lambda2)));
  }

}
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