Tuning skew_normal() parameters

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I was trying to model some data with asym_laplace() and with skew_normal(). The latter’s pp_check looks much better:

Can anyone advise how to additionally tune the parameters to get even better results? How would an example code/model look like?

Thanks!

• Operating System: macOS Ventura 13.3.1
• brms Version: 2.19.0