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

Correction to: Anim Biotelemetry (2020) 8:26 https://doi.org/10.1186/s40317-020-00213-z

Following publication of the original article [1], the authors identified an error in the equations.

This has been corrected with this erratum.

Equations for the vitality model survival functions were misspecified in the article. For the Vitality (2009) model (Eq. 8), the correct formulation is as follows:

$$ S\left( t \right) = \left[ {\Phi \left( {\frac{1 - rt}{{\sqrt {u^{2} + s^{2} t} }}} \right) - e^{{\left( {\frac{{2u^{2} r^{2} }}{{s^{4} }} + \frac{2r}{{s^{2} }}} \right)}} \cdot \Phi \left( { - \frac{{1 + rt + \frac{{2u^{2} r}}{{s^{2} }}}}{{\sqrt {u^{2} + s^{2} t} }}} \right)} \right]e^{ - kt} . $$

(8)

For the Vitality (2013) model (Eq. 9), the correct formulation of the survival function is as follows:

$$ S\left( t \right) = \left[ {\Phi \left( {\frac{1 - rt}{{s\sqrt t }}} \right) - e^{{2r/s^{2} }}\Phi \left( { - \frac{1 + rt}{{s\sqrt t }}} \right)} \right]e^{{\left( { - \frac{\lambda \beta }{r}e^{ - 1/\beta } \left( {e^{rt/\beta } - 1} \right)} \right)}} . $$

(9)

Although the expressions for the vitality models were misspecified in the article, all the numerical and graphical results were reported correctly and the conclusions are unaffected.

The original article [1] has been updated.