On the Smoothing of Death Curves Using Mixtures of Probability Distributions

Lucia Zanotto , Ca' Foscari University of Venice
Adelchi Azzalini, University of Padua

The distribution of deaths by age can be seen as a probability density function. Inspired by Pearson's theory about mortality components, a three-component mixture model has been recently introduced. In most of the cases, its parameter trends are regular and smooth, but there is a set of situations where the coefficients exhibit non-negligible irregularities. Since mortality changes slowly, raw fluctuations in the coefficients paths are not appropriate if they are not justified by exceptional events. To preserve regularity along time, information regarding past and future needs to be taken into account. However, this is not possible by estimating the parameters for each year separately from the other years. In order to ensure regular trends, we consider a slightly different route where every coefficient of the mixture is expressed as a function of time. Specifically, instead of evaluating the model parameters separately at each year, the the time-related coefficients are estimated in a comprehensive procedure which embraces all years of a given population. This strategy ensures both regular and smooth parameters' trends and suitable fit of the mixture model for each year of the time series.

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 Presented in Session P3. Poster Session Migration, Economics, Environment, Methods, History and Policy