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RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION

Year 2017, Volume: 10 Issue: 1, 1 - 13, 31.01.2017

Abstract

In this paper, a novel cumulative distribution function (c:d:f:) for beta-pareto (BP) distribution, through two distinct practical frames, is developed. However, the presented models are obviously more pragmatic than the ones being demonstrated in previous works, in the case of extending the further relations.
Then, using the exhibited c.d.f.s, certain recurrence relations for the single and product moments of the order statistics of a random sample of size n arising from beta-Pareto distribution are derived.

References

  • Akinsete, A., Famoye, F. and Lee, C. (2008). The beta-Pareto distribution. Statistics, 42, 547-563.
  • Alshawarbeh, E., Lee, C. and Famoye, F. (2012). Beta-Cauchy distribution. Journal of Probability and Statistical Science, 10, 41-57.
  • Arnold B. C., Balakrishnan N. and Nagaraja H. N. (1992). A rst course in order statistics. John Wiley, New York.
  • Cordeiro, G. M. and Lemonte, A. J. (2011). The ?-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Computational Statistics and Data Analysis, 55, 1445-1461.
  • David H. A. and Nagaraja H. N. (2003). Order statistics. 3rd edn. John Wiley & Sons, New York.
  • Eugene N., Lee, C. and Famoye, F. (2002). The beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31(4), 497-512.
  • Famoye, F., Lee, C. and Olumolade O. (2005). The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2), 121-136.
  • Gradshteyn I. S. and Ryzhik I. M. (2007). Table of Integrals, Series, and Products. 7th Edition. Elsevier Inc.
  • Jones M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1), 1-43.
  • Malik H. J., Balakrishnan N. and Ahmed S. E. (1988). Recurrence relations and identities for moments of order statistics- I: Arbitrary continuous distributions. Commun. Statist. - Theo. Meth., 17, 2623- 2655.
  • Nadarajah S. and Gupta A. K. (2004). The beta Frechet distribution. Far East Journal of Theoretical Statistics, 14, 15-24.
  • Samuel P. and Thomas P. Y. (2000). An improved form of a recurrence relation on the product moments of order statistics. Commun. Statist. - Theo. Meth., 29, 1559- 1564.
  • Thomas P. Y. and Samuel P. (1996). A note on recurrence relations for the product moments of order statistics. Statistics & Probability Letters, 29, 245 - 249.
Year 2017, Volume: 10 Issue: 1, 1 - 13, 31.01.2017

Abstract

References

  • Akinsete, A., Famoye, F. and Lee, C. (2008). The beta-Pareto distribution. Statistics, 42, 547-563.
  • Alshawarbeh, E., Lee, C. and Famoye, F. (2012). Beta-Cauchy distribution. Journal of Probability and Statistical Science, 10, 41-57.
  • Arnold B. C., Balakrishnan N. and Nagaraja H. N. (1992). A rst course in order statistics. John Wiley, New York.
  • Cordeiro, G. M. and Lemonte, A. J. (2011). The ?-Birnbaum-Saunders distribution: An improved distribution for fatigue life modeling. Computational Statistics and Data Analysis, 55, 1445-1461.
  • David H. A. and Nagaraja H. N. (2003). Order statistics. 3rd edn. John Wiley & Sons, New York.
  • Eugene N., Lee, C. and Famoye, F. (2002). The beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 31(4), 497-512.
  • Famoye, F., Lee, C. and Olumolade O. (2005). The beta-Weibull distribution. Journal of Statistical Theory and Applications, 4(2), 121-136.
  • Gradshteyn I. S. and Ryzhik I. M. (2007). Table of Integrals, Series, and Products. 7th Edition. Elsevier Inc.
  • Jones M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13(1), 1-43.
  • Malik H. J., Balakrishnan N. and Ahmed S. E. (1988). Recurrence relations and identities for moments of order statistics- I: Arbitrary continuous distributions. Commun. Statist. - Theo. Meth., 17, 2623- 2655.
  • Nadarajah S. and Gupta A. K. (2004). The beta Frechet distribution. Far East Journal of Theoretical Statistics, 14, 15-24.
  • Samuel P. and Thomas P. Y. (2000). An improved form of a recurrence relation on the product moments of order statistics. Commun. Statist. - Theo. Meth., 29, 1559- 1564.
  • Thomas P. Y. and Samuel P. (1996). A note on recurrence relations for the product moments of order statistics. Statistics & Probability Letters, 29, 245 - 249.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Hossein Jabbari Khamnei This is me

Roghaye Makouyi This is me

Publication Date January 31, 2017
Acceptance Date January 12, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Khamnei, H. J., & Makouyi, R. (2017). RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION. Istatistik Journal of The Turkish Statistical Association, 10(1), 1-13.
AMA Khamnei HJ, Makouyi R. RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION. IJTSA. January 2017;10(1):1-13.
Chicago Khamnei, Hossein Jabbari, and Roghaye Makouyi. “RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION”. Istatistik Journal of The Turkish Statistical Association 10, no. 1 (January 2017): 1-13.
EndNote Khamnei HJ, Makouyi R (January 1, 2017) RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION. Istatistik Journal of The Turkish Statistical Association 10 1 1–13.
IEEE H. J. Khamnei and R. Makouyi, “RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION”, IJTSA, vol. 10, no. 1, pp. 1–13, 2017.
ISNAD Khamnei, Hossein Jabbari - Makouyi, Roghaye. “RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION”. Istatistik Journal of The Turkish Statistical Association 10/1 (January 2017), 1-13.
JAMA Khamnei HJ, Makouyi R. RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION. IJTSA. 2017;10:1–13.
MLA Khamnei, Hossein Jabbari and Roghaye Makouyi. “RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION”. Istatistik Journal of The Turkish Statistical Association, vol. 10, no. 1, 2017, pp. 1-13.
Vancouver Khamnei HJ, Makouyi R. RECURRENCE RELATION FOR THE MOMENTS OF ORDER STATISTICS FROM A BETA-PARETO DISTRIBUTION. IJTSA. 2017;10(1):1-13.