The Beta Moyal: An Useful Skew Distribution

For the first time, we propose a so-called beta Moyal distribution,
which generalizes the Moyal distribution, and study its properties.
We derive expansions for the cumulative distribution function as
a weighted power series of the Moyal cumulative distribution.
We provide a comprehensive mathematical treatment of the new model and derive
expansions for its moments, moment generating function, mean deviations,
density function of the order statistics and their moments. We discuss maximum
likelihood estimation of the model parameters. We illustrate the
superiority of the new distribution as compared to the beta normal,
skew-normal and Moyal distributions by means of two real data sets.