Abstract
This note investigates the negative dependence in frailty models. First, we show that the frailty variable and the overall population variable are negatively likelihood ratio dependent and derive an upper bound for the survival function of the population with higher frailty. Secondly, we prove that the DFR property and the logconvex hazard rate of the baseline variable imply the DLR property of the population variable. Finally, we further prove that the likelihood ratio order, hazard rate order and reversed hazard rate order between two frailty variables imply the likelihood ratio order, reversed hazard rate order, and hazard rate order between the corresponding overall population variables, respectively.
Original language | English |
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Pages (from-to) | 1433-1441 |
Number of pages | 9 |
Journal | Journal of Statistical Planning and Inference |
Volume | 138 |
Issue number | 5 |
DOIs | |
State | Published - 1 May 2008 |
Keywords
- DFR
- DLR
- Hazard rate order
- Likelihood ratio order
- NBU(2)
- Negatively likelihood ratio dependent
- Reversed hazard rate order
- Reversely regular of order 2