| Summary: | 碩士 === 東海大學 === 統計學系 === 107 === The concept of life table originated from the study of human longevity. It was presented as a subject peculiar to demography, actuarial science and public health. It is a model used to describe the process of population death and is similar to the statistical method in reliability theory. Human life is a random experiment, its outcomes, survival and death, are subject to death. A life table systematically records the life and death of a number of individuals in a certain population. Thus the elements in the life table are random variables. This study uses the mathematical formula derived from the life table random variables to interpret some important properties of the life table. The life table data in Taiwan is applied to verify the trend of these properties. Firstly, we clarify the structural characteristics of the life table, and use its derivatives to investigate some combinations among the force of mortality, survival probability and life expectancy. Secondly, we inspect the inverse relation between variability in the distribution of ages at death, and the rectangularity of the survival curves. Finally, a flexible model of mortality related to proportional-hazards and senescence-slowing is used for taking an inside look of the subtle characteristics of the life expectancy increasing. Historical data of Taiwan life table after 1950s shows that the survival curve appeared rectangularity gradually, and the variability in the distribution of ages at death is declining. Based on the life table data in Taiwan from 1998 to 2008, a hybrid model of mortality used for analyzing the life expectancy increasing of the elderly. We find the trend influence life expectancy increasing, of which 27% were affected by the decline in mortality, while 73% were affected by senescence-slowing, indicating the latter plays a pivotal role influence the life expectancy.
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