Computer Analysis of Stochastic Aging According to the Gompertz-Makeham Mortality Law

The main aim is to present stochastic computer analysis of the Gompertz-Makeham mortality law applied frequently in biology to approximate mortality rates in various species populations. The exponential time series with three different coefficients defined as the Gaussian uncorrelated random variables is analyzed and its first four central probabilistic moments are derived analytically from the definition as the functions of expectations and standard deviations of these coefficients. They are used further in the visualization of time fluctuations of the expectations, coefficients of variation, skewness, and kurtosis of the mortality rate. Computational experiments performed in the computer algebra system MAPLE compare all these characteristics for various combinations of the input coefficients of variation of the input randomness level. They document that probabilistic characteristics of the mortality rate highly depend upon the input probabilistic parameters combination, where Gaussian uncertainty within the exponent seems to be the most influential. The numerical approach explored in this work may be further extended towards some other probabilistic methods like simulation or perturbation-based algorithms, other probability distributions in time series coefficients, power or polynomial mortality laws with random coefficients as well as more advanced modeling of the mortality rate defined as some stochastic process using probability of transition in time.