Coherent forecasting of multiple-decrement life tables: a test using Japanese cause of death data

Planners in public and private institutions would like coherent forecasts of the components of age-specic mortality, such as causes of death. This has been di cult to achieve because the relative values of the forecast components often fail to behave in a way that is coherent with historical experience. In addition, when the group forecasts are combined the result is often incompatible with an all-groups forecast. It has been shown that cause-specic mortality forecasts are pessimistic when compared with all-cause forecasts (Wilmoth, 1995). This paper abandons the conventional approach of using log mortality rates and forecasts the density of deaths in the life table. Since these values obey a unit sum constraint for both conventional single-decrement life tables (only one absorbing state) and multiple-decrement tables (more than one absorbing state), they are intrinsically relative rather than absolute values across decrements as well as ages. Using the methods of Compositional Data Analysis pioneered by Aitchison (1986), death densities are transformed into the real space so that the full range of multivariate statistics can be applied, then back-transformed to positive values so that the unit sum constraint is honoured. The structure of the best-known, single-decrement mortality-rate forecasting model, devised by Lee and Carter (1992), is expressed in compositional form and the results from the two models are compared. The compositional model is extended to a multiple-decrement form and used to forecast mortality by cause of death for Japan

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations