SOA mortality table vs. Gompertz

Ok, I tried to imagine a reason why any of my four or five readers would be interested in how the Society of Actuaries Individual Annuity Mortality table could be modeled using a Gompertz equation for a 58 year old male.  I could come up with no plausible scenario where the probability is greater than zero.  Yet here we are.

I started looking the SOA table because Joe Tomlinson once tipped me off that the SS Life table (2013) that I used for stochastic longevity in my modeling was not very conservative (SOA assumes a healthier self-selecting cohort).  Here is an overlay of the SOA IAM table's probability density for a 58 year old against a Gompertz approximation of the same.  The key inputs, in case you ever need to know it, for the gompertz is a central tendency of 90 and a dispersion of 8.5.  For what it's worth, the inputs for doing the same thing with the SS2013 Life table are 85.5 and 10 respectively.  Not perfect but close enough for rough modeling if I need it; plus it's malleable.

Disclaimer: this is not a statistician's kind of work but that of an amateur hack.  If one were to ask me about something like a Pearson's distribution or whether I have a good handle of how skew and kurtosis fit the curve i could tell you (almost) nothing.  I'm just trying to make sure I have a tool that works more or less towards things I am trying to do...generally.  For the most part, even though I do not have a good grasp of the ideal math, I'm thinking that compared to a typical retiree -- that a) does not have a plan around longevity at all, or b) uses a simple single number for a planning range like "to age 82" or "to the SS average expectancy" -- I am just slightly, not much but slightly, ahead of the game.