Suppose I have three quantile values of a skew normal distribution. How do I calculate the parameters of the distribution?
For one simple example, suppose I know the 10%, 50%, and 90% points of the distribution. Is there a nice closed form for the skew normal distribution here? It seems plausible that this might be easier in the case where we a) have the 50% point or b) have symmetrical non-median points eg 10% and 90% instead of 10% and 60%.
Wikipedia claims that Mudholkar and Hutson (full text here) provides a version of the distribution with "a CDF that is easily inverted such that there is a closed form solution to the quantile function.” However, I can’t find the quantile function in that paper.
This answer proposes a numerical solution, but I'd like an analytical one.
Mudholkar, Govind S., and Alan D. Hutson. "The epsilon–skew–normal distribution for analyzing near-normal data." Journal of Statistical Planning and Inference 83.2 (2000): 291-309