Core functions and core divergences of regular distributions

Zdeněk Fabián; Igor Vajda

Kybernetika (2003)

  • Volume: 39, Issue: 1, page [29]-42
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Fabián, Zdeněk, and Vajda, Igor. "Core functions and core divergences of regular distributions." Kybernetika 39.1 (2003): [29]-42. <http://eudml.org/doc/33620>.

@article{Fabián2003,
abstract = {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.},
author = {Fabián, Zdeněk, Vajda, Igor},
journal = {Kybernetika},
keywords = {Johnson transforms; generalizedJohnson distributions; core function of distributions; core divergences of distributions; Johnson transform; generalized Johnson distribution},
language = {eng},
number = {1},
pages = {[29]-42},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Core functions and core divergences of regular distributions},
url = {http://eudml.org/doc/33620},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Fabián, Zdeněk
AU - Vajda, Igor
TI - Core functions and core divergences of regular distributions
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 1
SP - [29]
EP - 42
AB - 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.
LA - eng
KW - Johnson transforms; generalizedJohnson distributions; core function of distributions; core divergences of distributions; Johnson transform; generalized Johnson distribution
UR - http://eudml.org/doc/33620
ER -

References

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  1. Fabián Z., 10.1109/18.568724, IEEE Trans. Inform. Theory 43 (1997), 1080–1083 (1997) MR1454240DOI10.1109/18.568724
  2. Fabián Z., 10.1081/STA-100002096, Commun. Statist. A – Theory Methods 30 (2001), 3, 537–556 Zbl1009.62534MR1862941DOI10.1081/STA-100002096
  3. Johnson N. L., 10.1093/biomet/36.1-2.149, Biometrika 36 (1949), 149–176 (1949) MR0033994DOI10.1093/biomet/36.1-2.149
  4. Johnson N. L., Kotz S., Continuous Univariate Distributions 1, 2, Houghton Mifflin, Boston 1970 
  5. Zacks S., The Theory of Statistical Inference, Wiley, New York 1971 Zbl0321.62003MR0420923

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