# What is meant by "empirical survival" in Taleb's Tail Risk of Contagious Diseases paper?

Nassim Taleb e.a. published a paper Tail Risk of Contagious Diseases which contains the following plot, based on 62 historical disease outbreaks:

I think I understand Zipf's law from the Wikipedia example, which plots word rank vs. word frequency:

But I'm confused about the units used in Taleb's chart. What is "empirical survival" here?

• Someone on Twitter pointed me here, so I'll read that: en.wikipedia.org/wiki/Empirical_distribution_function Commented Mar 25, 2020 at 15:19
• Survival function is 1-CDF, empirical survival indicates 1 - empirical CDF. Commented Mar 25, 2020 at 15:22
• My guess would be the Kaplan-Meier empirical survival function described in en.wikipedia.org/wiki/Kaplan%E2%80%93Meier_estimator. In any case, you can check against the numbers in Appendix 1. Commented Mar 25, 2020 at 16:45

Survival function is 1-CDF, empirical survival indicates 1 - empirical CDF
So for the first dot we have 1 element in the sample, so we get 1 - 1/62 = 0.98. For the second dot we have two elements in the sample, so 1 - 2/62 = 0.97, ..., the fourth is 1 - 4/62 = 0.93.