On characterization of distributions through the properties of conditional expectations of order statistics

Bairamov I., Ozkal T.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.36, no.7, pp.1319-1326, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 7
  • Publication Date: 2007
  • Doi Number: 10.1080/03610920601076990
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1319-1326
  • Keywords: characterizations of distributions, order statistics, progressively type-II censored order statistics
  • Dokuz Eylül University Affiliated: Yes

Abstract

For a general class of distributions some characterizations through the properties of conditional expectations of order statistics and progressively Type-II censored order statistics are given. Let X-1:n, X-2:n,..., X-n:n be the order statistics of the sample X-1, X-2,..., X-n from a continuous distribution and X-1:m:n(R), X-2:m:n(R),..., X-m:m:n(R) be the progressively Type-II censored order statistics with the progressively Type-II censoring scheme R = (R, R,..., R). We show that in this case, the joint distribution of X-1:m:n(R),..., X-m:m:n(R) can be reduced to the joint distribution of usual order statistics of a sample size m from a continuous random variable.