On Bayesian estimation in an exponential distribution under random censorship

Michal Friesl; Jan Hurt

Kybernetika (2007)

  • Volume: 43, Issue: 1, page 45-60
  • ISSN: 0023-5954

Abstract

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The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied via simulations in the special case.

How to cite

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Friesl, Michal, and Hurt, Jan. "On Bayesian estimation in an exponential distribution under random censorship." Kybernetika 43.1 (2007): 45-60. <http://eudml.org/doc/33839>.

@article{Friesl2007,
abstract = {The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied via simulations in the special case.},
author = {Friesl, Michal, Hurt, Jan},
journal = {Kybernetika},
keywords = {exponential distribution; random censoring; survival data analysis; reliability; Koziol–Green model; Bayesian estimates; Bayesian risk; conjugate priors; asymptotic properties; small sample properties; simulation study},
language = {eng},
number = {1},
pages = {45-60},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On Bayesian estimation in an exponential distribution under random censorship},
url = {http://eudml.org/doc/33839},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Friesl, Michal
AU - Hurt, Jan
TI - On Bayesian estimation in an exponential distribution under random censorship
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 1
SP - 45
EP - 60
AB - The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied via simulations in the special case.
LA - eng
KW - exponential distribution; random censoring; survival data analysis; reliability; Koziol–Green model; Bayesian estimates; Bayesian risk; conjugate priors; asymptotic properties; small sample properties; simulation study
UR - http://eudml.org/doc/33839
ER -

References

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  2. Franz J., On Estimation Problems in Random Censored Repair Models, Econom. Quality Control 9 (1994), No. 3, 125–142 (1994) Zbl0813.62086
  3. Friesl M., Weak asymptotics of the Bayes estimator of the reliability function in the Koziol–Green model, Statist. Decisions 19 (2001), 1, 83–87 Zbl0971.62009MR1817223
  4. Herbst T., Test of fit with the Koziol–Green model for random censorship, Statist. Decisions 10 (1992), 163–171 (1992) Zbl0746.62018MR1165711
  5. Hurt J., Comparison of some reliability estimators in the exponential case under random censorship, In: Proc. 5th Pannonian Symp. on Math. Statist. (W. Grossmann, J. Mogyoródí, and W. Wertz, eds.), Visegrád 1985, pp. 255–266 (1985) MR0956703
  6. Hurt J., Asymptotic expansions for moments of functions of stochastic processes and their Applications, Statist. Decisions 4 (1992), 251–271 (1992) MR0848330
  7. Hurt J., On Statistical Methods for Survival Data Analysis, In: Proc. Summer School ROBUST’92 (J. Antoch and G. Dohnal, eds.), Union of the Czech Mathematicians and Physicists, Prague 1992, pp. 54–74 (1992) 
  8. Koziol J. A., Green S. B., A Cramér–von Mises statistic for randomly censored data, Biometrika 63 (1976), 465–474 (1976) Zbl0344.62018MR0448695
  9. Liang T., Empirical Bayes estimation with random right censoring, Internat. J. Inform. Manag. Sci. 15 (2004), 4, 1–12 Zbl1069.62007MR2111199
  10. Martz H. F., Waller R. A., Bayesian Reliability Analysis, Wiley, New York 1982 Zbl0763.62053MR0670595
  11. Raqab M. Z., Madi M. T., 10.1080/00949650412331299166, J. Statist. Comput. Simulation 75 (2005), 10, 841–852 Zbl1167.62386MR2191325DOI10.1080/00949650412331299166
  12. Sarhan A. M., 10.1016/S0096-3003(01)00334-4, Appl. Math. Comput. 135 (2003), 2–3, 319–332 Zbl1016.62118MR1937256DOI10.1016/S0096-3003(01)00334-4

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