The inverse distribution for a dichotomous random variable
Bona, Elisabetta ; Sacchetti, Dario
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 385-394 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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 $(0,a)$, $\,a\in \Bbb R^{+}$. 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.

Publié le : 1997-01-01
Classification:  60E05,  60E10,  62E10,  62E15 
@article{118938,
     author = {Elisabetta Bona and Dario Sacchetti},
     title = {The inverse distribution for a dichotomous random variable},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {385-394},
     zbl = {0890.60014},
     mrnumber = {1455507},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118938}
}

Bona, Elisabetta; Sacchetti, Dario. The inverse distribution for a dichotomous random variable. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 385-394. http://gdmltest.u-ga.fr/item/118938/

Dieudonné J. Infinitesimal Calculus, Houghton Hifflin, Boston, 1971. | MR 0349286

Guest P.B. Laplace transforms and an introduction to distributions, Series mathematics and its applications, Ellis Horwood, 1991. | MR 1287158 | Zbl 0734.44002

Mora M. Classification des functions-variance cubiques des families exponentielles, C.R. Acad. Sci. Paris 302 sér. 1, 16 (1986), 582-591. (1986) | MR 0844163

Letac G.; Mora M. Natural real exponential families with cubic variance functions, The Annals of Statistics 18 (1990), 1-37. (1990) | MR 1041384 | Zbl 0714.62010

Morris C.N. Natural exponential families with quadratic variance functions, The Annals of Statistics 10 (1982), 65-80. (1982) | MR 0642719 | Zbl 0498.62015

Sacchetti D. Inverse distributions: an example of non existence, Accademia di scienze, lettere ed arti di Palermo, 1993.

Serrecchia A. Inverse distributions, Publ. de l'Inst. de Stat. de l'Univ. de PARIS XXXI 1 (1986), 71-85. (1986) | MR 0903423 | Zbl 0651.62010

Seshadri V. The Inverse Gaussian Distribution, Clarendon Press, Oxford, 1993. | MR 1306281 | Zbl 0942.62011

Tweedie H.C.K. Inverse statistical deviates, Nature (1945), 155-453. (1945) | MR 0011907