Statistical Papers

, Volume 47, Issue 3, pp 373–392

# Bayesian estimation and prediction for some life distributions based on record values

• M. Doostparast
Articles

## Abstract

Some statistical data are most easily accessed in terms of record values. Examples include meteorology, hydrology and athletic events. Also, there are a number of industrial situations where experimental outcomes are a sequence of record-breaking observations. In this paper, Bayesian estimation for the two parameters of some life distributions, including Exponential, Weibull, Pareto and Burr type XII, are obtained based on upper record values. Prediction, either point or interval, for future upper record values is also presented from a Bayesian view point. Some of the non-Bayesian results can be achieved as limiting cases from our results. Numerical computations are given to illustrate the results.

## Key words

Bayesian inference Beta function Conjugate prior Gamma distribution Jefferys prior Pivotal quantity

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## References

1. 1.
Ahmadi, J. (2000) Record Values, Theory and Applications, Ph. D. Dissertation, Ferdowsi University of Mashhad, Iran.Google Scholar
2. 2.
Ahmadi, J. and Arghami, N. R. (2001) On the Fisher information in record values, Metrika 53, 195–206.
3. 3.
Ahmadi, J. and Arghami, N. R. (2003a) Comparing the Fisher information in record values and iid observations. Statistics 37, 435–441.
4. 4.
Ahmadi, J. and Arghami, N. R. (2003b) Nonparametric confidence and tolerance intervals based on record data, Statist. Papers, 44, 455–468.
5. 5.
Ahmadi, J., Doostparast, M. and Parsian, A. (2005) Estimation and prediction in a two parameter exponential distribution based on k-record values under LINEX loss function, to appear in Commun. Statist. Theor. Meth. 34.Google Scholar
6. 6.
Ahmadi, J. and Balakrishnan, N. (2004) Confidence intervals for quantiles in terrms of record range, Statist. Probab. Lett., 68, 398–405.
7. 7.
Ahsanullah, M. (1980) Linear prediction of record values for the two parameter exponential distribution, Ann. Inst. Statist. Math., 32, 363–368.
8. 8.
Al-Hussaini, E. K. and Jaheen, Z. F. (1995) Bayesian prediction bounds for the Burr type XII faliure model. Commun. Statist. Theor. Meth. 24, 1829–1842.
9. 9.
Al-Hussaini, E. K. (1999) Predicting observable from a general class of distributions, J. Statist. Plann. Inference., 79, 79–91.
10. 10.
Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998) Records, John Wiley, New York.
11. 11.
Arnold, B. C. and Press, S. J. (1989) Bayesian estimation and prediction for Pareto data. J. Amer. Statist. Assoc. 84, 1079–1084.
12. 12.
Berger, J. O. (1980) Statistical Decision Theory Foundations, Concepts and Methods Probability. Springer-Verlag, New York Heidelberg Berlin.Google Scholar
13. 13.
Berred A. M. (1998) Prediction of record values. Commun. Statist. Theor. Meth. 27, 2221–2240.
14. 14.
Carlin, P. B. and Gelfand, A. E. (1993) Parametric likelihood inference for record breaking problems, Biometrika, 80, 507–515.
15. 15.
Chandler, K. N. (1952) The distribution and frequency of record values, J. Roy. Stat. Soc., B, 14, 220–228.
16. 16.
Dunsmore, I. R. (1983) The future occurrence of records, Ann. Inst. Statist. Math., 35, 267–277.
17. 17.
Feuerverger, A. and Hall, P. (1998) On statistical inference based on record values, Extremes, 12, 169–190.
18. 18.
Glick, N. (1978) Breaking records and breaking boards. Amer. Math. Monthly, 85, 2–26.
19. 19.
Gulati, S. and Padgett, W. J. (1994) Smooth nonparametric estimation of the distribution and density functions from record-breaking data. Commun. Statist. Theor. Meth, 23, 1259–1274.
20. 20.
Matiz, J. L. and Lwin, T. (1989) Emprical Bayes Methods, 2nd ed. Chapman & Hall, London.Google Scholar
21. 21.
Nevzorov, V. (2001) Records: Mathematical Theory. Translation of Mathematical Monographs. Volume 194. Amer. Math. Soc. Providence, RI. USA.Google Scholar