Gini coefficient as a life table function

This paper presents a toolkit for measuring and analyzing inter-individual inequality in length of life by Gini coefficient. Gini coefficient and four other inequality measures are defined on the length-of-life distribution. Properties of these measures and their empirical testing on mortality data suggest a possibility for different judgements about the direction of changes in the degree of inequality by using different measures. A new computational procedure for the estimation of Gini coefficient from life tables is developed and tested on about four hundred real life tables. The estimates of Gini coefficient are precise enough even for abridged life tables with the final age group of 85+. New formulae have been developed for the decomposition of differences between Gini coefficients by age and cause of death. A new method for decomposition of age-components into effects of mortality and composition of population by group is developed. Temporal changes in the effects of elimination of causes of death on Gini coefficient are analyzed. Numerous empirical examples show: Lorenz curves for Sweden, Russia and Bangladesh in 1995, proportional changes in Gini coefficient and four other measures of inequality for the USA in 1950-1995 and for Russia in 1959-2000. Further shown are errors of estimates of Gini coefficient when computed from various types of mortality data of France, Japan, Sweden and the USA in 1900-95, decompositions of the USA-UK difference in life expectancies and Gini coefficients by age and cause of death in 1997. As well, effects of elimination of major causes of death in the UK in 1951-96 on Gini coefficient, age-specific effects of mortality and educational composition of the Russian population on changes in life expectancy and Gini coefficient between 1979 and 1989. Illustrated as well are variations in life expectancy and Gini coefficient across 32 countries in 1996-1999 and associated changes in life expectancy and Gini coefficient in Japan, Russia, Spain, the USA, and the UK in 1950-1999. Variations in Gini coefficient, with time and across countries, are driven by historical compression of mortality, but also by varying health and social patterns.inequality, life expectancy, mortality, variability

Algorithm for decomposition of differences between aggregate demographic measures and its application to life expectancies, healthy life expectancies, parity-progression ratios and total fertility rates

A general algorithm for the decomposition of differences between two values of an aggregate demographic measure in respect to age and other dimensions is proposed. It assumes that the aggregate measure is computed from similar matrices of discrete demographic data for two populations under comparison. The algorithm estimates the effects of replacement for each elementary cell of one matrix by respective cell of another matrix. Application of the algorithm easily leads to the known formula for the age-decomposition of differences between two life expectancies. It also allows to develop new formulae for differences between healthy life expectancies. In the latter case, each age-component is split further into effects of mortality and effects of health. The application of the algorithm enables a numerical decomposition of the differences between total fertility rates and between parity progression ratios by age of the mother and parity. Empirical examples are based on mortality data from the USA, the UK, West Germany, and Poland and on fertility data from Russia.healthy life expectancy, life expectancy, parity progression

Estimates of mortality and population changes in England and Wales over the two World Wars

Almost one million soldiers from England and Wales died during the First and Second World War whilst serving in the British Armed Forces. Although many articles and books have been published that commemorate the military efforts of the British Armed Forces, data on the demographic aspects of British army losses remain fragmentary. Official population statistics on England and Wales have provided continuous series on the civilian population, including mortality and fertility over the two war periods. The combatant population and combatant mortality have not been incorporated in the official statistics, which shows large out-migration at the beginning and large in-migration towards the end of the war periods. In order to estimate the dynamics of the total population and its excess mortality, we introduce in this paper a model of population flows and mortality in times of war operations. The model can be applied to a detailed reconstruction of war losses, using various shapes of the input data. This enables us to arrive at detailed estimates of war-related losses in England and Wales during the two world wars. Our results agree with elements of data provided by prior studies.England, First World War, population estimates, Second World War, Wales

The stress state of the rock mass with spherical cavity

One of the main hypotheses accepted in the mechanics of deformable solids is the assumption of the homogeneity of materials. This means that all mechanical characteristics of the material (modulus of elasticity, Poisson’s ratio, yield strength, relaxation parameters, etc.) are constant over the volume of the body, in other words, these characteristics are constants. This hypothesis makes it possible not to take into account the natural inhomogeneity of materials at the microlevel - the presence of various fractions in composite materials (concrete, fiberglass, etc.), crystal lattice defects, etc. Examples can be given when various physical phenomena (temperature field, radiation exposure, explosive impact, etc.) lead to a change in the mechanical characteristics along the body. These changes can be quite significant. So, for example, in the presence of high-gradient temperature fields, the deformation characteristics of materials at different points of the body can change dozens of times. Thus, when calculating and designing structures, it is necessary to take into account such macro heterogeneity, since it leads to a significant change in the stress-strain state of bodies. This article considers the problem associated with the continuous inhomogeneity of materials. It means such a heterogeneity that arose in the process of creating an underground cavity with the help of an explosion. In contrast to the classical mechanics of a deformable solid body, the problems of which are reduced to differential equations with constant coefficients, in the mechanics of continuously inhomogeneous bodies we deal with equations with variable coefficients, which greatly complicates their solution. In this case, depending on the type of inhomogeneity functions—functions that describe the change in mechanical characteristics along the coordinates—differential equations turn out to be significantly different

Long-term trends in the longevity of scientific elites: evidence from the British and the Russian academies of science.

National science academies represent intellectual elites and vanguard groups in the achievement of longevity. We estimated life expectancy (LE) at age 50 of members of the British Royal Society (RS) for the years 1670-2007 and of members of the Russian Academy of Sciences (RAS) for the years 1750-2006. The longevity of academicians was higher than that of their corresponding national populations, with the gap widening from the 1950s. Since the 1980s, LE in the RS has been higher than the maximum LE among all high-income countries. In each period, LE in the RS was greater than in the RAS, although since the 1950s it has risen in parallel in the two academies. This steep increase shared by academicians in Britain and Russia suggests that general populations have the potential for a substantial increase in survival to high ages

Calculation of radially inhomogeneous ring loaded with normal and tangential loads

The aim of the study is to solve the problem of the stress-strain state of a thin ring under radial and ring loads, factoring in the radial inhomogeneity of the ring. Also, the task is to compare the two calculation methods to the example of solving the problem of uneven load distribution along the outer surface of the ring with one-dimensional inhomogenuity. Analytical or numerical-analytical solutions are used in the two-dimensional plane problem of the theory of elasticity in polar coordinates for an inhomogeneous body. Most of these problems consider centrally symmetric circular bodies. As a rule, this is possible when all unknown functions depend on the radius. These tasks correspond with the majority of ring and cylindrical structures. Pipes are suitable for creating pipeline systems and civil engineering, they are used for gas pipelines, in heating networks and water supply systems. The key feature of the work lies in the consideration of uneven radial and ring loads distribution along the outer surface of the ring. Comparison of the calculation results obtained by two methods makes it possible to determine the stressed and deformed states with sufficient accuracy, an indicator of which is the obtaining of the ring stresses