13. Survival Distributions and Failure Times

  1. S. David Promislow

Published Online: 13 JAN 2011

DOI: 10.1002/9781119971528.ch13

Fundamentals of Actuarial Mathematics, Second Edition

Fundamentals of Actuarial Mathematics, Second Edition

How to Cite

Promislow, S. D. (2010) Survival Distributions and Failure Times, in Fundamentals of Actuarial Mathematics, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971528.ch13

Author Information

  1. York University, Toronto, Canada

Publication History

  1. Published Online: 13 JAN 2011
  2. Published Print: 17 DEC 2010

ISBN Information

Print ISBN: 9780470684115

Online ISBN: 9781119971528



  • stochastic model - survival distributions and failure times;
  • survival distributions - stochastic model for mortality replacing deterministic model;
  • last-survivor annuities, or second-death insurances - failure time, time of second death;
  • multiple-decrement theory;
  • hazard function, or hazard rate - or intensity function or failure function;
  • continuous case, in applications - time of failure, not restricted to integers;
  • exponential distribution - family of distributions, and constant hazard function;
  • Gompertz–Makeham distribution - hazard function for human mortality, increase with age;
  • shifted distributions - and shifted random variables;
  • stochastic life table - stochastic model and deterministic model for mortality


This chapter contains sections titled:

  • Introduction to survival distributions

  • The discrete case

  • The continuous case

  • Examples

  • Shifted distributions

  • The standard approximation

  • The stochastic life table

  • Life expectancy in the stochastic model

  • Stochastic interest rates

  • Notes and references

  • Exercises