Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1152356 | Statistics & Probability Letters | 2012 | 8 Pages |
Abstract
Let X1,X2X1,X2, and X3X3 be independent random variables with absolutely continuous distributions having the common support [0,∞)[0,∞). We show that if X1≤hr[mrl,lr]X3 and X2≤hr[mrl,lr]X3, then max{X1,X2}≤hr[mrl,lr]max{X1,X3}. We also show that if X2≤rh[lr]X1 and X2≤rh[lr]X3, then min{X1,X2}≤rh[lr]min{X1,X3}. These results generalize and extend some of the results given in Shaked and Shanthikumar (2007, Example 1.C.36, p. 56), Joo and Mi (2010), and Da et al. (2010).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Neeraj Misra, Amit Kumar Misra,