Reliability Properties of Seven Parameters Burr XII Distribution
El-Bassiouny Ahmed Habib *, Abdo Abd El Latef Noura Fakhry
Mathematics Department, Faculty of Science, Mansoura University,
Mansoura, Egypt
*e-mail: el_bassiouny@mans.edu.eg
Received:
Received: 26 January 2010; revised: 13 September 2010; accepted: 16 September 2010; published online: 12 October 2010
DOI: 10.12921/cmst.2010.16.02.127-133
OAI: oai:lib.psnc.pl:719
Abstract:
This paper investigates reliability properties of a flexible extended (seven parameters) Burr XII family of distributions. Moreover, closed forms for n-th moments are derived.
Key words:
Burr XII distribution, moments and quantiles, reliability function
References:
[1] B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A first course in order statistics. NewYork, Wiley (1992).
[2] B.C. Arnold, The Pareto Distribution. International Cooperative Publishing House. Fairland, MD (1983).
[3] S. Kotz, S. Nadarajah, Extreme value theory, theory and applications. Singapore, World Scientific Publishing Company (2001).
[4] N. Balakrishnan, H.J. Malik, S. Puthenpura, Best linear unbiased estimation of location and scale parameters of the log-logistic distribution. Commn. Statist. – theory meth. 16(12), 3477-3495 (1987).
[5] N. Balakrishnan, M. Ahsanullah, Relations for single and product moments of record values from Lomax distribution. Sankhya, The Indian Journal of Statistics 56 B, Pt. 2, 140-146 (1994).
[6] A.H. El-Bassiouny, N.F. Abdo, Reliability properties of extended Makeham distributions. Computational Methods in Science and Technology 15(2), 143-149 (2009).
[7] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, series, and Products (6th ed.). Academic Press, San Diego 2000).
[8] A.W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84, 641-652 (1997).
[9] A.K. Olapade, On a six-parameter generalized Burr XII distribution. arXiv:0806.1579v1 [math.ST] (2008).
[10] S.M. Ross, Stochastic processes. second edition, New York, Wiley (1996).
[11] P.R. Tadikamalla, A look at the Burr and related distributions. International Statist. Rev. 48, 337-344 (1980).
This paper investigates reliability properties of a flexible extended (seven parameters) Burr XII family of distributions. Moreover, closed forms for n-th moments are derived.
Key words:
Burr XII distribution, moments and quantiles, reliability function
References:
[1] B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A first course in order statistics. NewYork, Wiley (1992).
[2] B.C. Arnold, The Pareto Distribution. International Cooperative Publishing House. Fairland, MD (1983).
[3] S. Kotz, S. Nadarajah, Extreme value theory, theory and applications. Singapore, World Scientific Publishing Company (2001).
[4] N. Balakrishnan, H.J. Malik, S. Puthenpura, Best linear unbiased estimation of location and scale parameters of the log-logistic distribution. Commn. Statist. – theory meth. 16(12), 3477-3495 (1987).
[5] N. Balakrishnan, M. Ahsanullah, Relations for single and product moments of record values from Lomax distribution. Sankhya, The Indian Journal of Statistics 56 B, Pt. 2, 140-146 (1994).
[6] A.H. El-Bassiouny, N.F. Abdo, Reliability properties of extended Makeham distributions. Computational Methods in Science and Technology 15(2), 143-149 (2009).
[7] I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, series, and Products (6th ed.). Academic Press, San Diego 2000).
[8] A.W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84, 641-652 (1997).
[9] A.K. Olapade, On a six-parameter generalized Burr XII distribution. arXiv:0806.1579v1 [math.ST] (2008).
[10] S.M. Ross, Stochastic processes. second edition, New York, Wiley (1996).
[11] P.R. Tadikamalla, A look at the Burr and related distributions. International Statist. Rev. 48, 337-344 (1980).
