Mid –Truncated Burr XII Distribution and Its Applications in Order Statistics

  • Jagdish Saran University of Delhi, Delhi - 110007, India.
  • Narinder Pushkarna University of Delhi, Delhi-110007, India
  • Shikha Sehgal University of Delhi, Delhi - 110007, India.
DOI: https://doi.org/10.19139/soic.v7i1.368
Keywords: Order Statistics, Mid-Truncated Burr XII Distribution, Single Moments, Product Moments, Recurrence Relations, Incomplete Beta Function, Characterization

Abstract

In this paper we define the Mid-Truncated Burr XII distribution and derive some of its statistical properties such as moments, moment generating function, characteristic function, likelihood function, etc. We have also obtained the recurrence relations for single and product moments of order statistics in a random sample of size n drawn from Mid-Truncated Burr XII distribution. Further, the characterization of mid truncated distribution using conditional moments has been given.

Author Biographies

Jagdish Saran, University of Delhi, Delhi - 110007, India.
Professor,Department of Statistics, University of Delhi, Delhi - 110007, India.
Narinder Pushkarna, University of Delhi, Delhi-110007, India
Department of Statistics, Ramjas college, University of Delhi, Delhi-110007, India
Shikha Sehgal, University of Delhi, Delhi - 110007, India.
Department of Statistics, University of Delhi, Delhi - 110007, India.

References

N. Balakrishnan, and P.C. Joshi, Moments of order statistics from doubly truncated power function distribution, Aligarh Journal of Statistics, vol. 1, no. 2, pp. 1498-1505, 1981.

N. Balakrishnan, H.J. Malik, and S. Ahmed, Recurrence relations and identities for moment of order statistics-II: Specific continuous distributions, Commun. Statist. Theory Meth., vol. 17, no. 8, pp. 2657-2694, 1988.

I.W. Burr, Cumulative frequency functions, Annals of Mathematical Statistics, vol. 13, pp. 215-232, 1942.

H.A. David and H.N. Nagaraja, Order Statistics, Third Edition, John Wiley & Sons, 2003.

M. Hashempour, Evidences in lifetimes of sequential r-out-of n systems and optimal sample size determination for Burr XII populations, Statistics Opt. Inform. Comput., vol. 5, pp. 147-157, 2017.

J.S. Huang, Moment problem of order statistics: A review, Inter. Statist. Rev., vol. 57, pp. 59-66, 1989.

J.S. Huang, and G.D. Lin, Characterizations of distributions by linear combinations of order statistics, Bull. Inst. Math., Academia Sinica, vol. 12, pp. 179-202, 1984.

A.H. Khan, and I.A. Khan, Moments of order statistics from Burr XII distribution and its characterizations, Metron, vol. XLV-N1-2,no. 30, pp. 21-29, 1987.

G.D. Lin, The product moments of order statistics with applications to characterizations of distributions, J. Statist. Plan. Infer., vol.21, pp. 395-406, 1989.

H.J. Malik, Exact moments of order statistics from a power function distribution, Secand. Act. J., pp. 64-69, 1967.

.M.M. Mohie El-Din, M.A.W. Mahmoud, and K.S. Sultan, On moment generating function of order statistics for doubly truncated

exponential distribution, Metron, vol. LIII, pp. 171-183, 1995.

M.M. Mohie El-Din, and K.S. Sultan, Recurrence relations between any continuous function of order statistics for doubly truncated continuous distributions and its applications, The Egyptian Statistical Journal, vol. 37, pp. 336-345, 1993.

M.M. Mohie El-Din, M.M. Amein, and A.M. Abd El-Raheem, On mid – truncated distributions and its applications, J. Adv. Res.App. Math., vol. 5, no. 2, pp. 20-38, 2013.

H. Okasha, M.M. Mohie-El-Din, and M. Mahmoud, On mid – truncated distributions and its applications in order statistic, J. Adv. Res. Stat. Probab., vol. 3, no. 2, pp. 47-57, 2011.

A. Pathak, and A. Chaturvedi, Estimation of the reliability function for two-parameter exponentiated Rayleigh or Burr type X distribution, Statistics Opt. Inform. Comput., vol. 2, pp. 305-322, 2014.

K. Pearson, E.S. Pearson, and N.L. Johnson, Tables of the incomplete beta function, Second Edition, 1968.

J. Saran, and N. Pushkarna, Moments of order statistics from doubly truncated generalized exponential distribution, Aligarh Journal of Statistics, vol. 19, pp. 77-82, 1999.

J. Saran, and N. Pushkarna, Moments of order statistics from doubly truncated linear-exponential distribution, Journal of the Korean Statistical Society, vol. 28, no. 3, pp. 279-296, 1999.

J. Saran, and N. Pushkarna, Recurrence relations for moments of progressive type-II right censored order statistics from Burr distribution, Statistics: Journal of theoretical and Applied Statistics, vol. 35, no. 4, pp. 495-507, 2001.

A.A. Soliman, Estimation of parameters of life from progressively censored data using Burr-XII Model, IEEE Transactions on Reliability, vol. 54, pp. 34-42, 2005.

G.J. Tortora, B.R. Funke, and C.L. Case, Microbiology An Introduction, Eighth Edition, Pearson Education, 2004.

Published
2019-01-07
How to Cite
Saran, J., Pushkarna, N., & Sehgal, S. (2019). Mid –Truncated Burr XII Distribution and Its Applications in Order Statistics. Statistics, Optimization & Information Computing, 7(1), 171-191. https://doi.org/10.19139/soic.v7i1.368
Issue
Vol 7 No 1 (2019)
Section
Research Articles
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