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Inverse distributions: the logarithmic case

Dario Sacchetti — 1998

Commentationes Mathematicae Universitatis Carolinae

In this paper it is proved that the distribution of the logarithmic series is not invertible while it is found to be invertible if corrected by a suitable affinity. The inverse distribution of the corrected logarithmic series is then derived. Moreover the asymptotic behaviour of the variance function of the logarithmic distribution is determined. It is also proved that the variance function of the inverse distribution of the corrected logarithmic distribution has a cubic asymptotic behaviour.

The inverse distribution for a dichotomous random variable

Elisabetta Bona;  Dario Sacchetti — 1997

Commentationes Mathematicae Universitatis Carolinae

In this paper we will deal with the determination of the inverse of a dichotomous probability distribution. In particular it will be shown that a dichotomous distribution admit inverse if and only if it corresponds to a random variable assuming values ( 0 , a ) , a ∈ ℝ + . Moreover we will provide two general results about the behaviour of the inverse distribution relative to the power and to a linear transformation of a measure.

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