What probability distribution’s diagram is similar to the body shape of a Caspian Sea Seal? I mean a distribution which is rounded in the middle, and tapered at the both ends. Different distribution parameters make it change its shape (different skewness & kurtosis).
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Johnson SU (or SB) distribution is your sea seal. You can play with gamma and delta parameters to make it skewed and fatter tailed. It's a transformation of a normal variable, very easy to deal with.