TY - JOUR
T1 - Right spread order of the second-order statistic from heterogeneous exponential random variables
AU - Zhao, Peng
AU - Li, Xiaohu
AU - Da, Gaofeng
PY - 2011/1
Y1 - 2011/1
N2 - Let X1,..., Xn be independent exponential random variables with respective hazard rates λ1,..., λn, and Y1,..., Yn be i.i.d. exponential random variables with common hazard rate λ. It is proved that X 2:n, the second order statistic from X1,..., X n, is larger than Y2:n, the second order statistic from Y1,...,Yn, with respect to the right spread order if and only if λ≥2n-1/n(n-1)(Σi=1n1/∧-n-1/ ∧(1)) with ∧(1) and Σi=1nλ i and ∧i = ∧(1) - λi, and X 2:n is smaller than Y2:n with respect to the right spread order if and only if λ ≤ Σi=1n - max 1≤i≤nλi/n-1 Further, the case with proportional decreasing hazard rate is also studied, and the results obtained here form nice extensions to some corresponding ones known in the literature.
AB - Let X1,..., Xn be independent exponential random variables with respective hazard rates λ1,..., λn, and Y1,..., Yn be i.i.d. exponential random variables with common hazard rate λ. It is proved that X 2:n, the second order statistic from X1,..., X n, is larger than Y2:n, the second order statistic from Y1,...,Yn, with respect to the right spread order if and only if λ≥2n-1/n(n-1)(Σi=1n1/∧-n-1/ ∧(1)) with ∧(1) and Σi=1nλ i and ∧i = ∧(1) - λi, and X 2:n is smaller than Y2:n with respect to the right spread order if and only if λ ≤ Σi=1n - max 1≤i≤nλi/n-1 Further, the case with proportional decreasing hazard rate is also studied, and the results obtained here form nice extensions to some corresponding ones known in the literature.
KW - Hazard rate order
KW - Likelihood ratio order
KW - MRL order
KW - Majorization order
KW - Order statistics
KW - p-Larger order
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U2 - 10.1080/03610926.2010.493277
DO - 10.1080/03610926.2010.493277
M3 - Article
AN - SCOPUS:79960377989
SN - 0361-0926
VL - 40
SP - 3070
EP - 3081
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 17
ER -