| Title:
|
Core functions and core divergences of regular distributions (English) |
| Author:
|
Fabián, Zdeněk |
| Author:
|
Vajda, Igor |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
[29]-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Johnson transforms |
| Keyword:
|
generalizedJohnson distributions |
| Keyword:
|
core function of distributions |
| Keyword:
|
core divergences of distributions |
| MSC:
|
62B10 |
| MSC:
|
62E10 |
| MSC:
|
62E15 |
| idZBL:
|
Zbl 1243.62016 |
| idMR:
|
MR1980122 |
| . |
| Date available:
|
2009-09-24T19:50:54Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135506 |
| . |
| Reference:
|
[1] Fabián Z.: Information and entropy of continuous random variables.IEEE Trans. Inform. Theory 43 (1997), 1080–1083 MR 1454240, 10.1109/18.568724 |
| Reference:
|
[2] Fabián Z.: Induced cores and their use in robust parametric estimation.Commun. Statist. A – Theory Methods 30 (2001), 3, 537–556 Zbl 1009.62534, MR 1862941, 10.1081/STA-100002096 |
| Reference:
|
[3] Johnson N. L.: Systems of frequency curves generated by methods of translations.Biometrika 36 (1949), 149–176 MR 0033994, 10.1093/biomet/36.1-2.149 |
| Reference:
|
[4] Johnson N. L., Kotz S.: Continuous Univariate Distributions 1, 2.Houghton Mifflin, Boston 1970 |
| Reference:
|
[5] Zacks S.: The Theory of Statistical Inference.Wiley, New York 1971 Zbl 0321.62003, MR 0420923 |
| . |
