I have a statistical sample where D10 = 8 (10% of population under the value 8), D50 = 11 (median), and D90 = 18 (90% of population under de value 18)
Now, I need to fit the $\mu$ and the $\sigma^2$ of a probability distribution given these values. Judging from the different distance of D10, and D90, from D50, I would discard the normal distribution. I think its more similar to a lognormal one.
Any help is highly appreciated