Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.
@article{bwmeta1.element.bwnjournal-article-zmv26i4p467bwm,
author = {Z. Grudzie\'n and D. Szynal},
title = {Characterizations of power distributions via moments of order statistics and record values},
journal = {Applicationes Mathematicae},
volume = {26},
year = {1999},
pages = {467-475},
zbl = {0993.62004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv26i4p467bwm}
}
Grudzień, Z.; Szynal, D. Characterizations of power distributions via moments of order statistics and record values. Applicationes Mathematicae, Tome 26 (1999) pp. 467-475. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv26i4p467bwm/
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