On the Generalized Lognormal Distribution

الملخص EN

This paper introduces, investigates, and discusses the γ-order generalized lognormal distribution (γ-GLD).

Under certain values of the extra shape parameter γ, the usual lognormal, log-Laplace, and log-uniform distribution, are obtained, as well as the degenerate Dirac distribution.

The shape of all the members of the γ-GLD family is extensively discussed.

The cumulative distribution function is evaluated through the generalized error function, while series expansion forms are derived.

Moreover, the moments for the γ-GLD are also studied.