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Analysis of the empirical distribution of the residuals derived from fitting the Heligman and Pollard curve to mortality data. (English) Zbl 1277.62100

Herrerías Pleguezuelo, Rafael (ed.) et al., Distribution models theory. Selected papers based on the presentations at the 5th workshop of Spanish Scientific Association of Applied Economy on distribution models theory, Granada, Spain, September 2005. Hackensack, NJ: World Scientific (ISBN 981-256-900-6/hbk). 243-283 (2006).
Summary: 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 modern, 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 ime 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.
For the entire collection see [Zbl 1100.91002].

MSC:

62G07 Density estimation
62E15 Exact distribution theory in statistics
62N02 Estimation in survival analysis and censored data
91D10 Models of societies, social and urban evolution
91B82 Statistical methods; economic indices and measures
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