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CHARACTERIZATION ORDERING RESULTS FOR LARGEST ORDER STATISTICS FROM HETEROGENEOUS AND HOMOGENEOUS EXPONENTIATED GENERALIZED GAMMA VARIABLES

Published online by Cambridge University Press:  27 June 2018

Abedin Haidari  and
Amir T. Payandeh Najafabadi
Abedin Haidari
Affiliation:
Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran E-mail: [email protected], [email protected]
Amir T. Payandeh Najafabadi
Affiliation:
Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran E-mail: [email protected], [email protected]
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Abstract

The main aim of this paper is to present two new results concerning the characterization of likelihood ratio and reversed hazard rate orders between largest order statistics from two sets of independent heterogeneous and homogeneous exponentiated generalized gamma distributed random variables. These characterization results complete and strengthen some previous ones in the literature.

Keywords

characterizationexponentiated generalized gamma distributionlikelihood ratio orderreversed hazard rate orderweighted arithmetic mean
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 3 , July 2019 , pp. 460 - 470
Copyright
Copyright © Cambridge University Press 2018 

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References

1.Balakrishnan, N. & Zhao, P. (2013). Hazard rate comparison of parallel systems with heterogeneous gamma components. Journal of Multivariate Analysis 113: 153–160.Google Scholar
2.Balakrishnan, N., Haidari, A. & Masoumifard, K. (2015). Stochastic comparisons of series and parallel systems with generalized exponential components. IEEE: Transactions on Reliability 64: 333–348.Google Scholar
3.Belzunce, F., Martínez-Riquelme, C. & Mulero, J. (2016). An introduction to stochastic orders. London: Academic Press.Google Scholar
4.Bon, J.L. & Paltanea, E. (2006). Comparison of order statistics in a random sequence to the same statistics with i.i.d. variables. ESAIM: Probability and Statistics 10: 1–10.Google Scholar
5.Cordeiro, G.M., Ortega, E.M.M. & Silva, G.O. (2009). The exponentiated generalized gamma distribution with application to lifetime data. Journal of Statistical Computation and Simulation 81: 827–842.Google Scholar
6.Dykstra, R.A., Kochar, S.C. & Rojo, J. (1997). Stochastic comparisons of parallel systems of heterogeneous exponential components. Journal of Statistical Planning and Inference 65: 203–211.Google Scholar
7.Fang, L. & Zhang, X. (2015). Stochastic comparisons of parallel systems with exponentiated Weibull components. Statistics and Probability Letters 97: 25–31.Google Scholar
8.Fang, R., Li, C. & Li, X. (2018). Ordering results on extremes of scaled random variables with dependence and proportional hazards. Statistics 52: 458–478.Google Scholar
9.Khaledi, B. & Kochar, S.C. (2000). Some new results on stochastic comparisons of parallel systems. Journal of Applied Probability 37: 1123–1128.Google Scholar
10.Kochar, S.C. & Xu, M. (2007). Stochastic comparisons of parallel systems when components have proportional hazard rates. Probability in Engineering and Informational Sciences 21: 597–609.Google Scholar
11.Kundu, A., Chowdhury, S., Nanda, A. & Hazra, N. (2016). Some results on majorization and their applications. Journal of Computational and Applied Mathematics 301: 161–177.Google Scholar
12.Mao, T. & Hu, T. (2010). Equivalent characterizations on orderings of order statistics and sample ranges. Probability in the Engineering and Informational Sciences 24: 245–262.Google Scholar
13.Marshall, A.W., Olkin, I. & Arnold, B.C. (2011). Inequalities: theory of majorization and its applications. New York: Springer-Verlag.Google Scholar
14.Misra, N. & Misra, A.K. (2013). On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components. Statistics and Probability Letters 83: 1567–1570.Google Scholar
15.Mitrinović, D.S. & Vasić, P.M. (1970). Analytic inequalities. Berlin: Springer-Verlag.Google Scholar
16.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer-Verlag.Google Scholar
17.Wang, J. (2017). Likelihood ratio ordering of parallel systems with heterogeneous scaled components. Probability in the Engineering and Informational Sciences: 1–9. https://doi.org/10.1017/S0269964817000249.Google Scholar
18.Zhao, P. & Balakrishnan, N. (2014). A stochastic inequality for the largest order statistics from heterogeneous gamma variables. Journal of Multivariate Analysis 129: 145–150.Google Scholar
19.Zhao, P. & Balakrishnan, N. (2015). Comparisons of largest order statistics from multiple-outlier gamma models. Methodology and Computing in Applied Probability 17: 617–645.Google Scholar
20.Zhao, P., Zhang, Y. & Qiao, J. (2016). On extreme order statistics from heterogeneous Weibull variables. Statistics 50: 1376–1386.Google Scholar