Skip to main content Accessibility help
×
Home
Hostname: page-component-66d7dfc8f5-rwwkz Total loading time: 0.399 Render date: 2023-02-09T01:00:39.684Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

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
Affiliation:
Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran E-mail: abedinhaidari@yahoo.com, amirtpayandeh@sbu.ac.ir
Amir T. Payandeh Najafabadi
Affiliation:
Department of Mathematical Sciences, Shahid Beheshti University, G.C. Evin, 1983963113, Tehran, Iran E-mail: abedinhaidari@yahoo.com, amirtpayandeh@sbu.ac.ir

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Balakrishnan, N. & Zhao, P. (2013). Hazard rate comparison of parallel systems with heterogeneous gamma components. Journal of Multivariate Analysis 113: 153160.CrossRefGoogle 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: 333348.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: 110.CrossRefGoogle 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: 827842.CrossRefGoogle 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: 203211.CrossRefGoogle Scholar
7.Fang, L. & Zhang, X. (2015). Stochastic comparisons of parallel systems with exponentiated Weibull components. Statistics and Probability Letters 97: 2531.CrossRefGoogle Scholar
8.Fang, R., Li, C. & Li, X. (2018). Ordering results on extremes of scaled random variables with dependence and proportional hazards. Statistics 52: 458478.CrossRefGoogle Scholar
9.Khaledi, B. & Kochar, S.C. (2000). Some new results on stochastic comparisons of parallel systems. Journal of Applied Probability 37: 11231128.CrossRefGoogle 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: 597609.CrossRefGoogle 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: 161177.CrossRefGoogle 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: 245262.CrossRefGoogle Scholar
13.Marshall, A.W., Olkin, I. & Arnold, B.C. (2011). Inequalities: theory of majorization and its applications. New York: Springer-Verlag.CrossRefGoogle 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: 15671570.CrossRefGoogle Scholar
15.Mitrinović, D.S. & Vasić, P.M. (1970). Analytic inequalities. Berlin: Springer-Verlag.CrossRefGoogle Scholar
16.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer-Verlag.CrossRefGoogle Scholar
17.Wang, J. (2017). Likelihood ratio ordering of parallel systems with heterogeneous scaled components. Probability in the Engineering and Informational Sciences: 19. 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: 145150.CrossRefGoogle Scholar
19.Zhao, P. & Balakrishnan, N. (2015). Comparisons of largest order statistics from multiple-outlier gamma models. Methodology and Computing in Applied Probability 17: 617645.CrossRefGoogle Scholar
20.Zhao, P., Zhang, Y. & Qiao, J. (2016). On extreme order statistics from heterogeneous Weibull variables. Statistics 50: 13761386.CrossRefGoogle Scholar
4
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

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

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

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

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *