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Table 1 Brief description of hazard functions for the nine failure–time models fit to the 42 sets of tag-life data plus the exponential function

From: Vitality models found useful in modeling tag-failure times in acoustic-tag survival studies

Failure–time functions Hazard function description
Exponential Constant over time
Weibull (2) Linear or log-linear monotonic increase/decrease
Weibull (3) Linear or log-linear monotonic increase/decrease with a shift that represents a guaranteed (“failure free”) period
Log-normal Monotonic decrease or dome-shaped
Log-logistic Monotonic decrease or dome-shaped. Allows for steeper decrease from apex than the log-normal
Gompertz Constant initial hazard, which can remain constant or then have a quadratic increase/decrease
Gamma Monotonic increase or decrease to a hazard rate of 1
Generalized gamma Monotonic increase or decrease to a specific hazard rate of \(\alpha\)
Vitality 2009 Initial hazard rate followed by a shift in rate
Vitality 2013 Initial hazard rate followed by a shift in rate