Geodesic
Core functions and core divergences of regular distributions
Kybernetika, Tome 39 (2003) no. 1, p. [29].

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

On bounded or unbounded intervals of the real line, we introduce classes of regular statistical families, called Johnson families because they are obtained using generalized Johnson transforms. We study in a rigorous manner the formerly introduced concept of core function of a distribution from a Johnson family, which is a modification of the well known score function and which in a one-to-one manner represents the distribution. Further, we study Johnson parametrized families obtained by Johnson transforms of location and scale families, where the location is replaced by a new parameter called Johnson location. We show that Johnson parametrized families contain many important statistical models. One form appropriately normalized $L_2$ distance of core functions of arbitrary distributions from Johnson families is used to define a core divergence of distributions. The core divergence of distributions from parametrized Johnson families is studied as a special case.
Classification : 62B10, 62E10, 62E15
Keywords: Johnson transforms; generalizedJohnson distributions; core function of distributions; core divergences of distributions 
@article{KYB_2003__39_1_a2,
     author = {Fabi\'an, Zden\v{e}k and Vajda, Igor},
     title = {Core functions and core divergences of regular distributions},
     journal = {Kybernetika},
     pages = {[29]},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2003},
     mrnumber = {1980122},
     zbl = {1243.62016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003__39_1_a2/}
}
TY  - JOUR
AU  - Fabián, Zdeněk
AU  - Vajda, Igor
TI  - Core functions and core divergences of regular distributions
JO  - Kybernetika
PY  - 2003
SP  - [29]
VL  - 39
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2003__39_1_a2/
LA  - en
ID  - KYB_2003__39_1_a2
ER  - 
%0 Journal Article
%A Fabián, Zdeněk
%A Vajda, Igor
%T Core functions and core divergences of regular distributions
%J Kybernetika
%D 2003
%P [29]
%V 39
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2003__39_1_a2/
%G en
%F KYB_2003__39_1_a2
Fabián, Zdeněk; Vajda, Igor. Core functions and core divergences of regular distributions. Kybernetika, Tome 39 (2003) no. 1, p. [29]. http://geodesic.mathdoc.fr/item/KYB_2003__39_1_a2/