Analysis of the empirical distribution of the residuals derived from fitting the Heligman and Pollard curve to mortality data

In studying the behaviour of human phenomena, it is of interest to examine the patterns that remain more or less stable, whether the comparison is made of different populations at a given moment or at different times, or of the same population in different situations. Such regularities have long been modelled, and this has enabled researchers to discover aspects and properties that are inherent to the phenomenon being studied. In the present paper, various techniques, some of which are relatively modem, are applied to the analysis of the empirical distribution of the residuals derived from fitting the Heligman and Pollard curve to mortality data. Firstly, we perform a graphical illustration from the time perspective (curves fitted over various periods) and then a static one for the ages (i.e. obtaining fits to different ages). The aim of this study is to explore the different distributions of the residuals at each age and thus to evaluate the correspondence between models (such as the Heligman and Pollard curve) and reality (the observed rates of mortality). For this purpose, we use graphical techniques, non-parametric techniques such as kernel smoothing,. splines and weighted local fit, and generalised additive models, together with bootstrap sampling techniques to describe distributions of statistical measures of the residuals.