Characterizations by power contractions of order statistics. (English) Zbl 1135.62006
Summary: Some general procedures are obtained to characterize the distribution of a sample of independent and identically distributed random variables by power contractions of the associated order statistics. Some necessary conditions for these kinds of relations are given, including some ordering properties. The results can also be applied to the family of distributions defined by M. C. Jones [Test 13, 1–43 (2004; Zbl 1110.62012)]. The general results are illustrated by obtaining known and new characterizations of some probability models.
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 62G30 | Order statistics; empirical distribution functions |
Citations:
Zbl 1110.62012References:
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