Stochastic properties of INID progressive Type-II censored order statistics

  • Authors:

  • Tiantian Mao;Taizhong Hu

  • Affiliations:

  • Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China;Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

Let X"1":"n@?X"2":"n@?...@?X"n":"n denote the order statistics of random variables X"1,X"2,...,X"n which are independent but not necessarily identically distributed (INID), and let K"1,K"2 be two integer-valued random variables, independent of {X"1,...,X"n}, such that 1@?K"1@?K"2@?n. It is shown that if K"1 has a log-concave probability function and SI(K"2|K"1) then RTI(X"K"""2":"n|X"K"""1":"n), and if K"2 has a log-concave probability function and SI(K"1|K"2) then LTD(X"K"""1":"n|X"K"""2":"n), where SI, RTI and LTD are three notions of bivariate positive dependence. Based on these, we obtain that RTI(X"j":"m","n^R|X"i":"m","n^R) and LTD(X"i":"m","n^R|X"j":"m","n^R) whenever 1@?i