Geodesic
Inverse distributions: the logarithmic case
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 785-795.

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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.
Classification : 60E05, 60F05, 62E10
Keywords: natural exponential family; Laplace transform; variance function 
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     author = {Sacchetti, Dario},
     title = {Inverse distributions: the logarithmic case},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {785--795},
     publisher = {mathdoc},
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     zbl = {1060.62504},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a13/}
}
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Sacchetti, Dario. Inverse distributions: the logarithmic case. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 785-795. http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a13/