# Bayesian analysis for the Burr type XII distribution based on record values

## DOI:

https://doi.org/10.6092/issn.1973-2201/3624## Abstract

In this paper we reviewed and extended some results that have been derived on record values from the two parameters Burr Type XII distribution. The two parameters were assumed to be random variables and Bayes estimates were derived on the basis of a linear exponential (LINEX) loss function. Estimates for future record values were derived using non Bayesian and Bayesian approaches. In the Bayesian approach we reviewed the estimators obtained by Ahmedi and Doostparast (2006) using the well known squared error loss (SEL) function and we derived estimate for the future record value under LINEX loss function. A numerical example with tables and figures illustrated the findings.## References

J. AHMADI, (2000), Record values, theory and applications. Ph.D. Thesis, Ferdowsi University of Mashhad, Mashhad, Iran.

J. AHMADI, M. DOOSTPARAST, (2006), Bayesian estimation and prediction for some life distributions based on record values, “Statistical Papers”, 47, vol. 3, pp. 373-392.

J. AHMADI, M. JOZANI, E. MARCHAND, A. PARSIAN, (2009), Prediction of k-records from a general class of distributions under balanced type loss functions, “Metrika”, 70, vol. 1, pp. 19-33.

E.K. AL-HUSSAINI, Z.F. JAHEEN, (1992), Bayesian estimation of the parameters, reliability and failure rate functions of the Burr Type XII failure model, “J. Statist. Comput. Simul.”, 41, pp. 1829-1842.

E.K. AL-HUSSAINI, Z.F. JAHEEN, (1995), Bayesian prediction bounds for the Burr Type XII failure model, “Commun. Statist. Theor. Meth.”, 24, pp. 1829-1842.

E.K. AL-HUSSAINI, M.A. MOUSSA, Z.F. JAHEEN, (1992), Estimation under the Burr type XII failure model based on censored data: A comparative study, “Test”, vol 1, pp. 33-42.

B.C. ARNOLD, N. BALAKRISHNAN, H.N. NAGARAJA, (1998), Records, John Wiley, New York.

M.A.M ALI MOUSA, (2001), Inference and prediction for the Burr Type X model based on Records, “Statistics”, 35, pp. 415-425.

A.M. AWAD, M.Z. RAQAB, (2000), Prediction intervals for the future record values from exponential distribution: comparative study, “J. Statist. Comput. Simul.”, 65, pp. 325-340.

P. BASAK, N. BALAKRISHNAN, (2003), Maximum likelihood prediction of future record statistic. Mathematical and statistical methods in reliability, in B.H. Lindquist and K.A. Doksun (eds.), “Series on Quality, Reliability and Engineering Statistics”, 7, Singapore: World Scientific Publishing, pp. 159-175.

I.W. BURR, (1942), Cumulative frequence functions, “Ann. Math. Statist.”, 13, pp. 215-232.

K.N. CHANDLER, (1952), The distribution and frequency of record values, “J. R. Stat. Soc. Series B”, 14, pp. 220-228.

M. DOOSTPARAST, J. AHMADI, (2006), Statistical analysis for geometric distribution based on records, “Computers & Mathematics with applications”, 52, pp. 905-916.

S.D. DUBBEY, (1972), Statistical contributions to reliability engineering, “ARL TR”, AD 774537, pp. 72-0120.

S.D. DUBBEY, (1973), Statistical treatment of certain life testing and reliability problems, “ARL TR”, AD 774537, pp. 73-0155.

W. FELLER, (1966), An Introduction to Probability Theory and its Applications, Vol. 2, second edition, John Wiley, New York.

S. GULATI, W.J. PADGETT, (1994), Smooth nonparametric estimation of the distribution and density functions from record breaking-data, “Commun. Statist. Theor. Meth.”, 23, vol. 5, pp. 259-1274.

M.I. HENDI, S.E. ABU-YOUSSEF, A.A ALRADDADI, (2007), A Bayesian Analysis of Record Statistics from the Rayleigh Model, “Intern. Mathem. Forum”, 2, vol. 13, pp. 619-631.

Z. F. JAHEEN, (2005), Estimation based on generalized order statistics from the Burr model. Commun. Statist. Theor. Meth. 34:785-794.

D. MOORE, A.S. PAPADOPOULOS, (2000), The Burr Type XII distribution as a failure model under various loss functions, “Microelectronics Reliability”, 40, pp. 2117-2122.

V. NEVZOROV, (2001), Records: mathematical theory, Translation of Mathematical Monographs. “Amer. Math. Soc.”, 194, Providence, RI.

A.S. PAPADOPOULOS, (1978), The Burr distribution as a failure model from a Bayesian approach, “IEEE Trans. Rel.”, R-27, vol. 5, pp. 369-371.

M.Z. RAQAB, J. AHMADI, M. DOOSTPARAST, (2007), Statistical inference based on record data from Pareto model, “Statistics”, 41, vol. 2, pp. 105-118.

H.R. VARIAN, (1975), A Bayesian approach to real estate assessment, in S.E. Finberg and A. Zellner (eds.), “Studies in Bayesian Econometrics and Statistics” in Honor of J. L. Savege, North Holland, Amesterdam, pp. 195-208.

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*Statistica*,

*71*(4), 421–435. https://doi.org/10.6092/issn.1973-2201/3624

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