The Gompertz-Makeham distribution

This work is about the Gompertz-Makeham distribution. The distribution has been applied plenty of times. The properties of the Gompertz-Makeham distribution investigated in this work are unimodality of the Gompertz-Makeham distribution and relationship between the median value and the mean residual life time of the Gompertz-Makeham distribution. For most of the realistic set of parameter values the function is unimodal but not for all. The example used in this work gives a set of parameter values for which the function is unimodal. The relationship between the median value and the mean life time, left after some given time, has also been investigated with truncation at fixed age S. A program for simulations of life time with the Gompertz-Makeham distribution has been written in Pascal. For the possibility to have estimators of the unknown parameters of the Gompertz-Makeham distribution the least square estimation has been applied by use of a program written in Pascal. Description of the least square estimation and also the method of Maximum Likelihood and the EMalgorithm are also included in this work. The estimators of parameters can also be obtained by use of the last two methods. For testing the hypothesis that extreme old ages follows the Gompertz-Makeham distribution a goodness of fit test has been applied to real demographic data. For this example the hypothesis that extreme old ages follows the Gompertz-Makeham distribution, with parameters estimated by use of the least square estimation, is rejected.