1. The limiting failure rate for a convolution of life distributions
- Author
-
Henry W. Block, Thomas H. Savits, and Naftali A. Langberg
- Subjects
failure rate function ,Statistics and Probability ,education.field_of_study ,decreasing failure rate ,Component (thermodynamics) ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Population ,Block (permutation group theory) ,Monotonic function ,Failure rate ,Limiting ,Reliability ,01 natural sciences ,increasing failure rate ,Convolution ,62N05 ,010104 statistics & probability ,convolution ,60K10 ,0101 mathematics ,Statistics, Probability and Uncertainty ,education ,Mathematics - Abstract
In this paper we investigate the limiting behavior of the failure rate for the convolution of two or more life distributions. In a previous paper on mixtures, Block, Mi and Savits (1993) showed that the failure rate behaves like the limiting behavior of the strongest component. We show a similar result here for convolutions. We also show by example that unlike a mixture population, the ultimate direction of monotonicity does not necessarily follow that of the strongest component.
- Published
- 2015