Properties of reverse hazard functions. (English) Zbl 1219.62160
Summary: For continuous distributions reverse hazard is defined as the probability density divided by the cumulative probability, \(F(x)\); whereas the usual hazard function is the density divided by the survivor function, \(1 - F(x)\). Reverse hazard corresponds to the conditional density of an immediate failure or state change, conditioned by the fact that the state change occurred. For example, of all the items that failed, the proportion of those items that immediately failed is reverse hazard. Reverse hazard exhibits many symmetrical properties with hazard. In this paper a set of theorems are developed that explicate the properties of reverse hazard for both continuous and discrete probability distributions. Taken together, hazard and reverse hazard are a powerful set of theoretical constructs that are valuable for understanding stochastic systems.
MSC:
| 62N99 | Survival analysis and censored data |
| 62P15 | Applications of statistics to psychology |
| 62B10 | Statistical aspects of information-theoretic topics |
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