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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