Abstract
Analogous to the Pearson system of distributions, Burr (1942) introduced a system that includes twelve types of CDFs which yield a variety of density shapes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdel-Hamid, A.H.: Constant-partially accelerated life tests for Burr XII distribution with progressive type II censoring. Comput. Stat. Data Anal. 53, 2511–2523 (2009)
AL-Hussaini, E.K.: A characterization of the Burr type XII distribution. Appl. Math. Lett. 1, 59–61 (1991)
AL-Hussaini, E.K.: Bayesian predictive density of order statistics based on finite mixture models. J. Stat. Plann. Infer. 113, 15–24 (2003)
AL-Hussaini, E.K.: Inference based on censored samples from exponentiated populations. Test 19, 487–513 (2010)
AL-Hussaini, E.K., Ahmad, A.A.: On Bayes interval prediction of future records. Test 12, 79–99 (2003)
AL-Hussaini, E.K., Hussein, M.: Estimation using censored data from exponentiated Burr type XII population. Open J. Stat. 1, 33–45 (2011)
AL-Hussaini, E.K., Jaheen, Z.F.: Bayes estimation of the parameters, reliability and failure rate functions of the Burr type XII failure model. J. Stat. Comput. Simul. 41, 31–49 (1992)
AL-Hussaini, E.K., Jaheen, Z.F.: Approximate Bayes estimators applied to the Burr model. Commun. Stat. Theory Meth. 23, 99–121 (1994)
AL-Hussaini, E.K., Jaheen, Z.F.: Bayes prediction bounds for the Burr type XII failure model. Commun. Stat. Theory Meth. 24, 1829–1842 (1995)
AL-Hussaini, E.K., Jaheen, Z.F.: Bayesian prediction bounds for the Burr type XII distribution in the presence of outliers. J. Stat. Plann. Infer. 55, 23–37 (1996)
AL-Hussaini, E.K., Mousa, M.A., Sultan, K.S.: Parametric and non-parametric estimation of P(Y < X) for finite mixtures of lognormal components. Commun. Stat. Theory Meth. 26, 1260–1289 (1997)
Burr, I.W.: Cumulative frequency functions. Ann. Math. Stat. 1, 215–232 (1942)
Burr, I.W., Cislak, P.J.: On a general system of distributions: I Its curve shaped characteristics, II. The sample median. J. Am. Stat. Assoc. 63, 627–635 (1968)
Drane, S.W., Owen, D.B., Seibetr, G.B.: The Burr distribution and quantal responses. Stat. Hefte 19, 204–210 (1978)
Dubey, S.D.: Statistical contributions to reliability engineering. ARL TR 72-0155, AD 1774537 (1972)
Dubey, S.D.: Statistical treatment of certain life testing and reliability problems. ARL TR 73-0155, AD 1774537 (1973)
Embrechts, P., Kluppelberg, C., Mikosch, T.: Modeling Extremal Events. Springer, Berlin (1977)
Evans, I.G., Ragab, A.S.: Bayesian inferences given a type-2 censored samples from Burr distribution. Commun. Stat. Theory Meth. 12, 1569–1580 (1983)
Gupta, R.C., Gupta, R.D.: On the distribution of order statistics for a random sample size. Stat. Neerlandica 38, 13–19 (1984)
Hatke, M.A.: A certain cumulative probability function. Ann. Math. Stat. 20, 461–463 (1949)
Jaheen Z.F.: Bayesian estimations and predictions based on single Burr type XII models and their finite mixture. Ph.D. dissertation, University of Assiut, Egypt (1990)
Khan, A.H., Khan, A.I.: Moments of order statistics from Burr’s distribution and its characterization. Metron 45, 21–29 (1987)
Klugman, A.S.: Loss distributions. In: Proceedings of Symposia in Applied Mathematics, vol. 35, pp. 31–55 (1986)
Lawless, J.F.: Statistical Models and Methods for Lifetime Data, 2nd edn. Wiley, New York (1983)
Lewis, A.W.: The Burr distribution as a general parametric family in survivorship and reliability theory and applications. Ph.D. thesis, University of North-Carolina, USA (1981)
Lindsay, S.R., Wood, G.R., Woollons, R.C.: Modeling the diameter distribution of forest stands using the Burr distribution. J. Appl. Stat. 23, 609–618 (1996)
Lingappaiah, G.S.: Bayesian approach to the estimation of parameters in the Burr’s XII distribution with outliers. J. Orissa Math. Soc. 1, 53–59 (1983)
McDonald, J.B.: Some generalized function for the size distribution of income. Econometrica 52, 247–663 (1984)
McDonald, J.B., Richards, D.O.: Model selection: Some generalized distributions. Commun. Stat. Theory Meth. 17, 287–296 (1978)
Moore, D., Papadopoulos, A.S.: The Burr type XII distribution as a failure model under various loss functions. Microelectron. Reliab. 40, 2117–2122 (2000)
Morrison, D.G., Schmittlein, D.C.: Jobs, strikes and wars: Probability models for duration. Organiza. Behav. Hum. Perform 25, 224–251 (1980)
Nigm, A.M.: Prediction bounds for the Burr model. Commun. Stat. Theory Meth. 17, 287–296 (1988)
Papadopoulos, A.S.: The Burr distribution as a life time model from a Bayesian approach. IEEE Trans. Rel. R-27, 369–371 (1978)
ParanÃaba, P.F., Ortega, E.M.M., Cordeiro, G.M., Pescim, R.R.: The beta Burr XII distribution with application to lifetime data. Comput. Stat. Data Anal. 55, 1118–1136 (2011)
Rodrigues, R.N.: A guide to the Burr type XII distributions. Biomerika 64, 129–134 (1977)
Shah, A., Gokhale, D.V.: On maximum product of spacings (MPS) estimation for Burr XII distribution. Commun. Stat. Theory Meth. 22, 615–641 (1993)
Shao, Q.: Estimation of hazardous concentrations based on NOEC toxicity data: an alternative approach. Environmetrics 11, 583–595 (2000)
Shao, Q., Wong, H., Xio, J., Ip, W.: Modes for extremes using the extended three parameter Burr XII system with application to flood frequency analysis. Hydrol. Sci. 49, 685–702 (2004)
Tadikamalla, P.R.: A look at the Burr and related distributions. Int. Stat. Rev. 48, 337–344 (1980)
Takahasi, K.: Note on multivariate Burr’s distribution. Ann. Inst. Stat. Math. 17, 257–260 (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Atlantis Press and the authors
About this chapter
Cite this chapter
AL-Hussaini, E.K., Ahsanullah, M. (2015). Family of Exponentiated Burr Type XII Distributions. In: Exponentiated Distributions. Atlantis Studies in Probability and Statistics, vol 5. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-079-9_5
Download citation
DOI: https://doi.org/10.2991/978-94-6239-079-9_5
Published:
Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-6239-078-2
Online ISBN: 978-94-6239-079-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)