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Expressions for moments of order statistics and records from the skew-normal distribution in terms of multivariate normal orthant probabilities

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  • Mahdi Salehi
  • Mahdi Doostparast

Abstract

In designs of experiments and reliability analyze, order statistics (OS) are used for various purposes including model checking, estimations of parameters and prediction. Most of these procedures are defined on the basis of expectations of OS problems. In this paper, explicit expressions for central moments of OS coming from the skew-normal (SN) distribution are derived. The SN model enjoys interesting properties from the normal distribution while captures asymmetric behavior in the parent population. Another important topic which is related to OS is record statistics. These data are arising in some practical situations including shock models, sports and epoch times of a non-homogeneous Poisson processes. Here, we derive moments of the upper and the lower record values arising from the skew normal distribution. The obtained results may be used for prediction purposes such as predictive maintenance in a repairable system and prediction of performance of a transmission oil pipeline. Some real data sets are analyzed using the results obtained for illustration purposes. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Mahdi Salehi & Mahdi Doostparast, 2015. "Expressions for moments of order statistics and records from the skew-normal distribution in terms of multivariate normal orthant probabilities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 547-568, November.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:4:p:547-568
    DOI: 10.1007/s10260-015-0306-y
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    References listed on IDEAS

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    1. Balakrishnan, N. & Chan, P. S., 1998. "On the normal record values and associated inference," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 73-80, July.
    2. Mahdi Salehi & Ahad Jamalizadeh & Mahdi Doostparast, 2014. "A generalized skew two-piece skew-elliptical distribution," Statistical Papers, Springer, vol. 55(2), pages 409-429, May.
    3. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 1-13, April.
    4. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    5. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    6. Nadarajah, Saralees, 2008. "Explicit expressions for moments of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 196-205, February.
    7. Mahdi Salehi & Jafar Ahmadi, 2014. "Record ranked set sampling scheme," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 351-365, October.
    8. Adelchi Azzalini & Antonella Bacchieri, 2010. "A prospective combination of phase II and phase III in drug development," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 347-369.
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    1. Mahdi Salehi & Andriette Bekker & Mohammad Arashi, 2023. "A Semi-parametric Density Estimation with Application in Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 52-78, April.

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