Longevity-related Statistics and Their Perturbation Analysis: A Markov Chain, Matrix Calculus Approach

点击翻译按钮获取中文摘要

Human longevity has always been a central focus of demographic research. It reflects the intensity, age pattern, and causes of mortality throughout the life cycle, from infant mortality to old-age mortality and everything in between. The objective of this research project is to develop and apply new mathematical tools for the sensitivity analysis of longevity. Sensitivity analysis quantifies the effects of changes, and these new tools will enable researchers to quantify the effects of changes in mortality on various statistics measuring longevity. Those statistics include life expectancy, indices of variation in longevity, and the contributions of particular causes of death to those statistics.Sensitivity analysis is important in the study of longevity because human mortality has changed dramatically over the last two centuries, due to unprecedented advances in medicine, public health, and technology. In addition to these temporal changes, at any one time, patterns of longevity also differ among regions, countries, and socio-economic groups. Together, these changes in longevity have important implications for society, determining, as they do, the age structure of populations and the needs for medical care and social services. The new analytical methods developed in this research will be widely useful in studies of changing longevity and its consequences.