Trends in the development of the life expectancy at births and modal age at deaths in European countries

People often consider the question of where the limits of the lengths of human life lie. Length of life is usually expressed as the life expectancy at births (or more generally the life expectancy at exact age x years). The values of the life expectancy at births and of the modal age at deaths differ from one another and their development trends in time also differ. This is due first and foremost to the fact that the life expectancy at births is the average age of deaths in the stationary population, which is strongly influenced by the extreme values, especially the level of infant mortality. In contrast to this, the modal age at deaths is given by the age at which people most frequently die (with the exception of childhood). The term modal age at deaths was already introduced by Ch. Bernoulli and defined precisely by Lexis (1877) as the age when the number of deaths in adulthood (in the life tables) attains its maximum. The modal age at deaths is often used as a characteristic of longevity. This paper will analyse and compare trends in the development of the life expectancy and the modal age at deaths in European countries using various methods for the smoothing and modelling the mortality at higher ages. An estimate will also be made of the possible future development of mortality with the help of the analysis of time series.