Abstract
We derive conditions for stochastic, hazard rate, likelihood ratio, reversed hazard rate, increasing convex and mean residual life orderings of Pareto distributions with different shape and scale parameters. A real data application of the conditions is presented.
This is a preview of subscription content, log in via an institution to check access.
References
Bae, S. J., Kim, S. J., Lee, J. H., Song, I., Kim, N. I., Seo, Y., et al. (2014). Degradation pattern prediction of a polymer electrolyte membrane fuel cell stack with series reliability structure via durability data of single cells. Applied Energy, 131, 48–55.
Balakrishnan, N., & Zhao, P. (2013). Ordering properties of order statistics from heterogeneous populations: A review with an emphasis on some recent developments (with discussion). Probability in the Engineering and Informational Sciences, 27, 403–467.
Fang, L., & Tang, W. (2014). On the right spread ordering of series systems with two heterogeneous Weibull components. Journal of Inequalities and Applications. doi:10.1186/1029-242X-2014-190.
Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions (Vol. 1). New York: Wiley.
Khaledi, B.-E., & Kochar, S. C. (2006). Weibull distribution: Some stochastic comparisons results. Journal of Statistical Planning and Inference, 136, 3121–3129.
Li, C., & Li, X. (2015). Likelihood ratio order of sample minimum from heterogeneous Weibull random variables. Statistics and Probability Letters, 97, 46–53.
Liu, J., Chen, W., Zhang, Y. J., & Cao, Z. (2013). A utility maximization framework for fair and efficient multicasting in multicarrier wireless cellular networks. IEEE/ACM Transactions on Networking, 21, 110–120.
R Development Core Team. (2016). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
Ramos Romero, H. M., & Sordo Diaz, M. A. (2001). The proportional likelihood ratio order and applications. Questiio, 25, 211–223.
Shaked, M., & Shanthikumar, J. G. (2007). Stochastic orders. New York: Springer.
Torrado, N. (2015). Comparisons of smallest order statistics from Weibull distributions with different scale and shape parameters. Journal of the Korean Statistical Society, 44, 68–76.
Warin, T., & Leiter, D. (2012). Homogenous goods markets: An empirical study of price dispersion on the internet. International Journal of Economics and Business Research, 4, 514–529.
Acknowledgements
The authors thank the editor and anonymous referees for their helpful comments, which contributed greatly to improve this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nadarajah, S., Jiang, X. & Chu, J. Comparisons of smallest order statistics from Pareto distributions with different scale and shape parameters. Ann Oper Res 254, 191–209 (2017). https://doi.org/10.1007/s10479-017-2444-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-017-2444-0