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Order Statistics from Non-Identical Standard Type II Generalized Logistic Variables and Applications at Moments

Received: 1 December 2014     Accepted: 28 December 2014     Published: 16 January 2015
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Abstract

In this paper the moment generating function of order statistics arising from independent non-identically distributed (INID) Standard type II Generalized logistic (SGLII) variables is established. A recurrence relation for all moments of all order statistics arising from INID SGLII is computed. Special cases for moments are deduced using polygamma function. Some numerical examples are given.

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 1)
DOI 10.11648/j.ajtas.20150401.11
Page(s) 1-5
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Moments, Nonidentically Order Statistics, Standard Type II Generalized Logistic distribution, Polygamma Function

References
[1] ABDELKADER, Y. (2004) Computing the moments of order statistics from nonidentically distributed Gamma variables with applications Int J Math Game Theo Algebra, 14.
[2] ABDELKADER, Y. (2008) Computing the moments of order statistics from independent nonidentically distributed Beta random variables. Stat Pap, 49, 136-149.
[3] BALAKRISHNAN, N. (1994) Order statistics from non-identically exponential random variables and some applications. Comput. in Statistics Data-Anal, 18, 203-253.
[4] BALAKRISHNAN, N. & HOSSAIN, A. (2007) Inference for the type II generalized logistic distribution under progressive type II censoring. Journal of statistical computation and simulation, 77, 1013-1031.
[5] BAPAT, R. B. & BEG, M. I. (1989) Order statistics from non-identically distributed variables and permanents. Sankh˜ya, A, 51, 79-93.
[6] BARAKAT, H. & ABDELKADER, Y. (2003) Computing the moments of order statistics from nonidentical random variables Stat Meth Appl, 13, 15-26.
[7] BARAKAT, H. M. & ABDELKADER, Y. H. (2000) Computing the moments of order statistics from nonidentically distributed Weibull variables. J. Comp. Appl. Math, 117, 85-90.
[8] CHILDS, A. & BALAKRISHNAN, N. (2006) Relations for order statistics from non-identical logistic random variables and assessment of the effect of multiple outliers on bias of linear estimators. J. Statist. Plann. Inference, 136, 2227-2253.
[9] DAVID, H. A. & NAGARAJA, H. N. (2003) Order Statistics, Third Edition. Wiley, New York.
[10] JAMJOOM, A. A. (2006) Computing the moments of order statistics from independent nonidentically distributed Burr type XII random variables. journal of Mathematics and Statistics, 2, 432-438.
[11] JAMJOOM, A. & AL-SAIARY. A. (2011) Moment Generating Function Technique for Moments of Order Statistics from Nonidentically Distributed Random variables. International journal of Statistics and Systems, 6, 177-188.
[12] MOHIE ELIDIN, M., MAHMOUD, M., MOSHREF, M. & MOHMED, M. (2007) On independent and nonidentical order statistics and associated inference. Department of mathematics. Cairo, Ai-Azhar University.
[13] VAUGHAN, R. J. & VENABLES, W. N. (1972) Permanent expressions for order statistics densities. J. R. Statist. Soc, 34, 08 - 10.
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  • APA Style

    Z. AL-Saiary. (2015). Order Statistics from Non-Identical Standard Type II Generalized Logistic Variables and Applications at Moments. American Journal of Theoretical and Applied Statistics, 4(1), 1-5. https://doi.org/10.11648/j.ajtas.20150401.11

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    ACS Style

    Z. AL-Saiary. Order Statistics from Non-Identical Standard Type II Generalized Logistic Variables and Applications at Moments. Am. J. Theor. Appl. Stat. 2015, 4(1), 1-5. doi: 10.11648/j.ajtas.20150401.11

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    AMA Style

    Z. AL-Saiary. Order Statistics from Non-Identical Standard Type II Generalized Logistic Variables and Applications at Moments. Am J Theor Appl Stat. 2015;4(1):1-5. doi: 10.11648/j.ajtas.20150401.11

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  • @article{10.11648/j.ajtas.20150401.11,
      author = {Z. AL-Saiary},
      title = {Order Statistics from Non-Identical Standard Type II Generalized Logistic Variables and Applications at Moments},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {1},
      pages = {1-5},
      doi = {10.11648/j.ajtas.20150401.11},
      url = {https://doi.org/10.11648/j.ajtas.20150401.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150401.11},
      abstract = {In this paper the moment generating function of order statistics arising from independent non-identically distributed (INID) Standard type II Generalized logistic (SGLII) variables is established. A recurrence relation for all moments of all order statistics arising from INID SGLII is computed. Special cases for moments are deduced using polygamma function. Some numerical examples are given.},
     year = {2015}
    }
    

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    AB  - In this paper the moment generating function of order statistics arising from independent non-identically distributed (INID) Standard type II Generalized logistic (SGLII) variables is established. A recurrence relation for all moments of all order statistics arising from INID SGLII is computed. Special cases for moments are deduced using polygamma function. Some numerical examples are given.
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Author Information
  • Department of Statistics, King Abdulaziz University, Sciences Faculty for Girls, Saudia Arabia

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