Most probable rupture force under a linear ramp ($F_{\ast }=\max \{0,F_0\log [f/(k_0{F}_0)]\}$)

Differentiate the logarithm of the rupture-force probability density $k(F)p(F)/f$. Its interior stationary point satisfies $e^{F/F_0}=f/(k_0{F}_0)$. The physical domain is $F\ge 0$, giving the displayed mode. This differs from the median rupture force under a linear ramp; replacing one by the other shifts a fitted intercept and can bias the inferred zero-force rate.