Life Length Data: Its Genesis and Characteristics

壽命期間數據: 數據生成及特點

Student thesis: Doctoral Thesis

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Award date10 Aug 2018

Abstract

By lifetime data we mean a collection of observation that are the realizations of non-negative independent random variables having a common distribution. Such data arise in the context of life testing, reliability, survival analysis, business, economics and the social sciences. By event history data, we mean a collection of observations that are the realizations of non-negative random variables which constitute the inter-arrival times of a stochastic point process. The non-negative random variables in a point process may or may not be independent and as such may or may not be generated by a common distribution. Event history data are generally encountered in the contexts of maintenance, repairs, and replacement; they also arise in the context of risk analysis spawned by natural and man made disasters. Both lifetime and event history data share a common feature in the sense that the random variables which generate the data are generally skewed.

In this dissertation we investigate aspects of the random variables mentioned above, and their distributions. We focus on three scenarios, two of which are suggested by applications, and the third a more conceptual and foundational consideration. The two application scenarios pertain to a use of lifetime data for diagnosis, and a use of event history data in maintenance. The conceptual scenario pertains to the use of lifetime data to study the interplay between notions in economic, reliability, and applied probability to characterize the probability distributions which generate these data.