Probability models are now a vital componentof every scienti c
investigation. This book is intended to introduce basic ideas in
stochastic modeling, with emphasis on models and techniques. These
models lead to well-known parametric lifetime distributions, such as
exponential, Weibull, and gamma distributions, as well as the
change-point and mixture models. They also motivate us to consider more
general notions of nonparametric lifetime distribution classes.
Particular attention has been paid to their applications in reliability,
insurance mathematics, and economics. The following topics are the focus
in this volume: 1. Exponential Distributions and the Poisson Process; 2.
Parametric Lifetime Distributions; 3. Nonparametric Lifetime
Distribution Classes; 4. Multivariate Exponential Extensions; 5.
Association and Dependence; 6. Renewal Theory; 7. Applications to
Reliability, Insurance, Finance, and Credit Risk.
Chapter1providesnotationandbasicresultsinprobabilitytheorythatareneeded
in the consequent chapters. Chapters 2 and 3 are devoted to models
related to exponential distribution and Poisson processes. Particular
attentions is paid to the characterizations of exponential distribution
and the Poisson process. Two of the most important properties that
characterize exponential distribution: the lack of memory property and
constant failure rate are discussed in detail. Then the g- eralizations
of exponential distribution are examined in three directions: through
its parametric form that leads to parametric families of lifetime
distributions; via notionsof aging(such as monotonefailure rate) that
lead to a varietyof lifetime d- tribution classes; and through lifetime
distributions of multiple component systems that lead to multivariate
(mainly bivariate) exponential extension.
