16. The Minimum Failure Time

  1. S. David Promislow

Published Online: 14 JAN 2011

DOI: 10.1002/9781119971528.ch16

Fundamentals of Actuarial Mathematics, Second Edition

Fundamentals of Actuarial Mathematics, Second Edition

How to Cite

Promislow, S. D. (2010) The Minimum Failure Time, in Fundamentals of Actuarial Mathematics, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971528.ch16

Author Information

  1. York University, Toronto, Canada

Publication History

  1. Published Online: 14 JAN 2011
  2. Published Print: 17 DEC 2010

ISBN Information

Print ISBN: 9780470684115

Online ISBN: 9781119971528

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Keywords:

  • minimum failure time;
  • associated single-decrement setting;
  • joint distributions;
  • joint survival function;
  • distribution of J from joint distribution;
  • hazard functions for (T, J);
  • nonidentifiability problem - two different distributions for (T1, T2);
  • common shock model - objects, future lifetimes independent, subject to common hazards;
  • copulas, concerned with situations - and lack of independence;
  • problems of choosing a copula - modeling a given situation

Summary

This chapter contains sections titled:

  • Introduction

  • Joint distributions

  • The distribution of T

  • The joint distribution of (T, J)

  • Other problems

  • The common shock model

  • Copulas

  • Notes and references

  • Exercises