Is there a metric that is commonly used with survival functions?
If not, is there any metric that weights divergence at earlier values of $t$ more than later values? Early failures are much less desirable than later ones, so it seems natural to devise a metric with such a property.
- If not, does it make sense to devise one, and does anyone have any pointers for doing this? I have some intuition that cdfs might naturally penalize early failures, but I don't know enough about the subject to get from there to a metric.