The study of mortality in age groups
by
Gheorghe Florin Cristian
Faculty of Science, "Valahia" University, Targoviste, Romania
Coauthors: Gheorghe Gabriela Silvia, Faculty of Medicine "Carol Davila" Bucharest, Romania

Researchers in the demographic field are concerned about the different aspects of the human mortality.

Death is not a repetitive event. It is attributed to a single cause. By studying mortality, we must take into account the simultaneous action of a number of risk factors upon the life of an individual. For instance, if more deaths are caused by tuberculosis in young people, there can be a lower number of deaths by heart diseases, in a definite interval of time. That is why there have been used some methods in order to establish the causes that produce deaths and also to establish the mortality index for the age groups. Unfortunately, the results of these studies were not always satisfactory for the demography.

It is obvious that, examining closely the implication of death phenomenom, we can notice that there is a similitude with the probabilistic notion of Markovian dependency and also with a more general dependency of Onicescu-Mihoc type.

Onicescu-Mihoc type of the statistical dependency takes into account the whole development of the process and contains the Markov type of dependency as a particular case, so when the phenomenon is studied, the application of a chain with complete links is required.

The first part of this paper deals with a theoretical statistic model which considers that the random variables {xt}t € N (where xt indicate the causes of deaths in the period of time t) are chained according to the probability law of a chain with complete links (an Onicescu-Mihoc chain).

The practical solution for the considered demographic model, the chains with complete links, presents some difficulties due to the fact that the statistic theory of estimation of the parameters that belong to components of the chain is incompletely developed.

That is why, in the second part of our paper, we deal with the same problem using regular Markov chain.

P. Damiani studied and published a mathematical model in the case of the Markov type of dependency, which takes into account the existent relationship between the mortality causes upon the age groups. This model was published in “The Trimestrial Bulletin of Institute of French Actuaries” in March 1973. The author supposes there is a link between the different mortality indexes. Further on, we are going to present the way in which we have completed this model, taking into account the theory of the competitive risks. For this purpose, we are going to individualize the generalized functions in the case of the chains with complete links and suppose that the row of the random variables {xt} forms a regular Markov chain

Date received: June 11, 2006