Statistical Methods with Applications to Demography and Life Insurance

Statistical Methods with Applications to Demography and Life Insurance

by Estate V. Khmaladze
Released March 2013
Publisher(s): Chapman and Hall/CRC
ISBN: 9781466505742

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Book description

Suitable for statisticians, mathematicians, actuaries, and students interested in the problems of insurance and analysis of lifetimes, Statistical Methods with Applications to Demography and Life Insurance presents contemporary statistical techniques for analyzing life distributions and life insurance problems. It not only contains traditional material but also incorporates new problems and techniques not discussed in existing actuarial literature.

The book mainly focuses on the analysis of an individual life and describes statistical methods based on empirical and related processes. Coverage ranges from analyzing the tails of distributions of lifetimes to modeling population dynamics with migrations. To help readers understand the technical points, the text covers topics such as the Stieltjes, Wiener, and Ito integrals. It also introduces other themes of interest in demography, including mixtures of distributions, analysis of longevity and extreme value theory, and the age structure of a population. In addition, the author discusses net premiums for various insurance policies.

Mathematical statements are carefully and clearly formulated and proved while avoiding excessive technicalities as much as possible. The book illustrates how these statements help solve numerous statistical problems. It also includes more than 70 exercises.

Table of contents

  1. Front Cover
  2. Contents
  3. Preface
  4. List of Figures
  5. List of Tables
  6. Lecture 1: Duration of life as a random variable (1/2)
  7. Lecture 1: Duration of life as a random variable (2/2)
  8. Lecture 2: Models of distribution functions F(x) and force of mortality μ(x) (1/3)
  9. Lecture 2: Models of distribution functions F(x) and force of mortality μ(x) (2/3)
  10. Lecture 2: Models of distribution functions F(x) and force of mortality μ(x) (3/3)
  11. Lecture 3: The empirical distribution function of duration of life (1/2)
  12. Lecture 3: The empirical distribution function of duration of life (2/2)
  13. Lecture 4: Deviation of Fn(x) from F(x) as a random process (1/2)
  14. Lecture 4: Deviation of Fn(x) from F(x) as a random process (2/2)
  15. Lecture 5: Limit of empirical process: Brownian bridge. Distribution of X2 goodness of fit statistic (1/3)
  16. Lecture 5: Limit of empirical process: Brownian bridge. Distribution of X2 goodness of fit statistic (2/3)
  17. Lecture 5: Limit of empirical process: Brownian bridge. Distribution of X2 goodness of fit statistic (3/3)
  18. Lecture 6: Statistical consequences of what we have learned so far. Two-sample problems (1/3)
  19. Lecture 6: Statistical consequences of what we have learned so far. Two-sample problems (2/3)
  20. Lecture 6: Statistical consequences of what we have learned so far. Two-sample problems (3/3)
  21. Lecture 7: Testing parametric hypotheses. Unexpected example – exponentiality of durations of rule of Roman emperors (1/4)
  22. Lecture 7: Testing parametric hypotheses. Unexpected example – exponentiality of durations of rule of Roman emperors (2/4)
  23. Lecture 7: Testing parametric hypotheses. Unexpected example – exponentiality of durations of rule of Roman emperors (3/4)
  24. Lecture 7: Testing parametric hypotheses. Unexpected example – exponentiality of durations of rule of Roman emperors (4/4)
  25. Lecture 8: Estimation of the rate of mortality (1/2)
  26. Lecture 8: Estimation of the rate of mortality (2/2)
  27. Lecture 9: Censored observations. Related point processes (1/2)
  28. Lecture 9: Censored observations. Related point processes (2/2)
  29. Lecture 10: Kaplan–Meier estimator (product-limit estimator) for F (1/3)
  30. Lecture 10: Kaplan–Meier estimator (product-limit estimator) for F (2/3)
  31. Lecture 10: Kaplan–Meier estimator (product-limit estimator) for F (3/3)
  32. Lecture 11: Statistical inference about F, based on the Kaplan–Meier estimator (1/4)
  33. Lecture 11: Statistical inference about F, based on the Kaplan–Meier estimator (2/4)
  34. Lecture 11: Statistical inference about F, based on the Kaplan–Meier estimator (3/4)
  35. Lecture 11: Statistical inference about F, based on the Kaplan–Meier estimator (4/4)
  36. Lecture 12: Life insurance and net premiums (1/4)
  37. Lecture 12: Life insurance and net premiums (2/4)
  38. Lecture 12: Life insurance and net premiums (3/4)
  39. Lecture 12: Life insurance and net premiums (4/4)
  40. Lecture 13: More on net premiums. Endowments and annuities (1/2)
  41. Lecture 13: More on net premiums. Endowments and annuities (2/2)
  42. Lecture 14: Annuities certain. Some problems of general theory (1/2)
  43. Lecture 14: Annuities certain. Some problems of general theory (2/2)
  44. Lecture 15: Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life (1/5)
  45. Lecture 15: Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life (2/5)
  46. Lecture 15: Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life (3/5)
  47. Lecture 15: Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life (4/5)
  48. Lecture 15: Right-tail behavior of Fn. Non-parametric confidence bounds for expected remaining life (5/5)
  49. Lecture 16: Population dynamics (1/4)
  50. Lecture 16: Population dynamics (2/4)
  51. Lecture 16: Population dynamics (3/4)
  52. Lecture 16: Population dynamics (4/4)
  53. Bibliography (1/2)
  54. Bibliography (2/2)

Product information

  • Title: Statistical Methods with Applications to Demography and Life Insurance
  • Author(s): Estate V. Khmaladze
  • Release date: March 2013
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781466505742