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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).
As you look at the chart, you can see the vertical axis represents some kind of Survival Function and horizontal axis defines War Casualties. As you can see, the higher the magnitude of Was Casualties, the lower the Survival rate/function and vice-versa. The higher the Survival rate the lower casualty count. Each dot represents each recording. Most likely, you need to look into how Survival Function is defined to really get a good understanding.
