The inverse distribution for a dichotomous random variable

Elisabetta Bona; Dario Sacchetti

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 385-394
  • ISSN: 0010-2628

Abstract

top
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.

How to cite

top

Bona, Elisabetta, and Sacchetti, Dario. "The inverse distribution for a dichotomous random variable." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 385-394. <http://eudml.org/doc/248047>.

@article{Bona1997,
abstract = {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 $(0,a)$, $\,a\in \mathbb \{R\}^\{+\}$. 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.},
author = {Bona, Elisabetta, Sacchetti, Dario},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {inverse measure; inverse probability distribution; Laplace transform; variance function; inverse measure; inverse probability distribution; Laplace transform; variance function},
language = {eng},
number = {2},
pages = {385-394},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The inverse distribution for a dichotomous random variable},
url = {http://eudml.org/doc/248047},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Bona, Elisabetta
AU - Sacchetti, Dario
TI - The inverse distribution for a dichotomous random variable
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 385
EP - 394
AB - 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 $(0,a)$, $\,a\in \mathbb {R}^{+}$. 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.
LA - eng
KW - inverse measure; inverse probability distribution; Laplace transform; variance function; inverse measure; inverse probability distribution; Laplace transform; variance function
UR - http://eudml.org/doc/248047
ER -

References

top
  1. Dieudonné J., Infinitesimal Calculus, Houghton Hifflin, Boston, 1971. MR0349286
  2. Guest P.B., Laplace transforms and an introduction to distributions, Series mathematics and its applications, Ellis Horwood, 1991. Zbl0734.44002MR1287158
  3. Mora M., Classification des functions-variance cubiques des families exponentielles, C.R. Acad. Sci. Paris 302 sér. 1, 16 (1986), 582-591. (1986) MR0844163
  4. Letac G., Mora M., Natural real exponential families with cubic variance functions, The Annals of Statistics 18 (1990), 1-37. (1990) Zbl0714.62010MR1041384
  5. Morris C.N., Natural exponential families with quadratic variance functions, The Annals of Statistics 10 (1982), 65-80. (1982) Zbl0498.62015MR0642719
  6. Sacchetti D., Inverse distributions: an example of non existence, Accademia di scienze, lettere ed arti di Palermo, 1993. 
  7. Serrecchia A., Inverse distributions, Publ. de l'Inst. de Stat. de l'Univ. de PARIS XXXI 1 (1986), 71-85. (1986) Zbl0651.62010MR0903423
  8. Seshadri V., The Inverse Gaussian Distribution, Clarendon Press, Oxford, 1993. Zbl0942.62011MR1306281
  9. Tweedie H.C.K., Inverse statistical deviates, Nature (1945), 155-453. (1945) MR0011907

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.