Preliminary studies of a new stochastic human death function involving small integers

We propose a new mathematical function for the analyses of age-related human deaths due to single causes. Like the earlier Gompertz and power law functions, it is a two parameter function. Unlike them, one of the parameters is an integer in the range of 5-13. The function is the integral gamma distribution raised to a combinatoric power (GDCP). The function has a deep relation to the power law, and this explains the past successes of the power law. The GDCP function generates highly accurate distributions for ages at death due to specific diseases, and also the means and variances for the distributions. It is possible now to assign unambiguously an integer to each cause of death. In model systems, the alpha integers are the number of "events" necessary to commit the organism to death. Different diseases with the same integer have the same age distribution at death. The major remaining problem is the relative sizes of the populations dying of each single cause. The solution to this must be model derived. The analysis of 24 single causes of death for males and females in the U.S.A., white population over the years 1968-1978 show: (1) the alpha integer is eight for almost all digestive organ carcinomas in both males and females; (2) cancers at other sites have various values for alpha; and (3) for vascular diseases females have alpha integers higher by one or two than males. If the combinatoric power is multiplied by a constant then the second number in the function, tau, the time constant, which is different for each disease, takes on an approximately constant value, which we call the "characteristic age" of the species. Thus, with one number, the "characteristic age" and the nine integers, we can predict, using the GDCP function, the relevant distributions of deaths due to all the different diseases.