# How to interpret this 'Zipf' (survival, war casualties) plot?

Help me interpret this chart please?

What do the X and Y axes mean here? (I asked the author directly but they didn't respond for some reason.)

Any thoughts on what 'Surivival Function' might mean here?

War Casualties from 1800 until today, n data points

Here, survival function $$Y'$$ shows the probability of survival for an individual when there is $$X'$$ war casualties. If $$X'$$ is close to zero, survival probability would be close to one.
When variable $$Y'$$ (survival function) depends on $$X'$$ (war casualties) based on Zipf's law, that means $$Y'=C'{X'}^{-\alpha}$$ which is a power-law relationship. If we take the logarithm of relationship, we have $$\text{log}Y'=-\alpha\text{log}X'+logC'$$ By setting $$X=\text{log}X'$$, $$Y=\text{log}Y'$$, and $$C=logC'$$, it becomes $$Y=-\alpha X + C$$ This means if we plot the logarithm of variables (log-log plot), we should see a line with negative slope. Of course, in real world scenarios, variables would follow this relationship approximately. For example, in the plot, the slope becomes closer to zero when $$X$$ is smaller.
Note that in the plot the values are still showing the original variables $$Y'$$ (between 0 and 1) and $$X'$$ (on the order of millions).