I am planning to assign a skewed normal distribution prior to one of the parameters \theta in my model. I know the mean \mu and standard deviation \sigma of that parameter and want to apply a weakly informative prior on the scale hyperparameter in the skewed normal distribution and let the model estimate it automatically.
The model I want to construct is \theta \sim skewednormal(\xi, \omega, \alpha), with known values of \xi and \alpha and assign a positive uniform prior on \omega.
However, given the three-hyperparameter in the skewed normal distribution, is it possible for me to know the exact value of hyperparameter \xi and \alpha based only on mean \mu and standard deviation \sigma, thus I could assign a positive uniform prior on the hyperparameter \omega?
Thanks so much for your help!