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FJ Rubio and MFJ Steel

On the Marshall-Olkin transformation as a skewing mechanism

Abstract: This note studies the use of the Marshall-Olkin transformation as a skewing mechanism. The distributions obtained when this transformation is applied to several classes of symmetric and unimodal distributions are analysed. It is shown that most of the resulting distributions are not flexible enough to model data presenting high or moderate skewness. The only case we encounter where the Marshall-Olkin transformation can be considered a useful skewing mechanism is when applied to Student-t distributions with Cauchy or even heavier tails.

Keywords: Moment; skewness measure; Student-t; tail behaviour.