my 2 cent: i have studied statistic (several exams), i just want point out here nobody can say no or yes, because nobody has made a study about it. Of course if you can believe Paradox, but this isn't a proof (anyway i'm not english speaker so i hope this is understable)
If you want make a proof you should take a large enough sample (how much is "enough" it depends) and you should start with some hyothesis, which should be proved of rejected. And you can't just see a chart and say "Hey there is a pattern!", you should use at least some of the statistic distribution to analyze if there is or not a correlation (i.e. the Chi squared
http://en.wikipedia.org/wiki/Chi-squared_distribution ).
When it comes to choice a sample, the idea is you should choice a sample which well-represent the experiment which you want make it (i.e. if you want study a correlation between election and poverty, you should choose poor people who can vote, if you choose kid or rich your data will be wrong). Normally you can define the sample about your hypothesis and reality, but in a game?
It really depends on your hypothesis only, so let say you think good king dies early (or better good king rule less than bad king) and you start take data from every religion, culture, tech and gov form. But you don't know if those things influence experiment (maybe Sunni iqta king die faster than French Catholic King, which can really screw your analysis). And you will never know if a general king died for the military code or for life_expectancy code.
So you can make a sample and analyze it, but it's probably your test will reach any conclusion, at least if you don't make many different test (and by the way this is why there scientist not agreeing about some result, because for them the sample or/and the hypothesis were wrong).
and please stop saying "my good king rule 50 years so no" because this prove nothing (as much as say "my good king rule 1 year so yes")
edit: if we have the code we could actually make an analysis to study the correlation between death and stat