It seems you've provided a complex mathematical expression, possibly from a statistical or analytical context, but it's not entirely clear what you're asking for. You might want to clarify aspects like:
- What specific distribution are you looking for? Are you looking for an analytical solution, a probability distribution function, or something else?
- Are there specific variables or parameters that are known, or do you need help understanding the relationships in your expression?
- Is there a particular context (e.g., signal processing, Bayesian analysis) that this expression pertains to?
Please provide additional details or clarify your question, and I'd be happy to assist you further!