Frequency functions of the form (1) below including Pearson's system as a special case are derived from a generating differential equation (2). Their properties are discussed, methods of fitting them are suggested, and their characteristic function is determined.
Fausto I. Toranzos. "An Asymmetric Bell-Shaped Frequency Curve." Ann. Math. Statist. 23 (3) 467 - 469, September, 1952. https://doi.org/10.1214/aoms/1177729393