Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T01:12:29.820Z Has data issue: false hasContentIssue false
  • English
  • Français

COMPARISONS OF SAMPLE RANGES ARISING FROM MULTIPLE-OUTLIER MODELS: IN MEMORY OF MOSHE SHAKED

Published online by Cambridge University Press:  29 December 2017

Narayanaswamy Balakrishnan ,
Jianbin Chen ,
Yiying Zhang  and
Peng Zhao
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Canada E-mail: [email protected]
Jianbin Chen
Affiliation:
LPMC and Institute of Statistics, Nankai University, Tianjin 300071, China E-mail: [email protected]
Yiying Zhang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China E-mail: [email protected]
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.

Keywords

majorization ordermultiple-outlier models,PHR modelsp-larger orderreversed hazard rate ordersample rangeusual stochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019 , pp. 28 - 49
Copyright
Copyright © Cambridge University Press 2017 

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. & Basu, A.P. (eds.) (1995). The exponential distribution: theory, methods and applications. Newark, New Jersey: Gordon and Breach.Google Scholar
2.Balakrishnan, N. & Torrado, N. (2016). Comparisons between largest order statistics from multiple-outlier models. Statistics 50: 176–189Google Scholar
3.Balakrishnan, N. & Rao, C.R. (eds.) (1998a). Handbook of statistics vol. 16: order statistics: theory and methods. Amsterdam: Elsevier.Google Scholar
4.Balakrishnan, N. & Rao, C.R. (eds.) (1998b). Handbook of statistics vol. 17: order statistics: applications. Amsterdam: Elsevier.Google Scholar
5.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models. Silver Spring, Maryland: To Begin With.Google Scholar
6.Bon, J.L. & Pǎltǎnea, E. (1999). Ordering properties of convolutions of exponential random variables. Lifetime Data Analysis 5: 185–192.Google Scholar
7.Ding, W., Da, G. & Zhao, P. (2013). On sample ranges from two sets of heterogenous random variables. Journal of Multivariate Analysis 116: 63–73.Google Scholar
8.Genest, C., Kochar, S.C. & Xu, M. (2009). On the range of heterogeneous samples. Journal of Multivariate Analysis 100: 1587–1592.Google Scholar
9.Khaledi, B.-E. & Kochar, S.C. (2001). Stochastic properties of spacings in a single-outlier exponential model. Probability in the Engineering and Informational Sciences 15: 401–408.Google Scholar
10.Kochar, S.C. & Rojo, J. (1996). Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions. Journal of Multivariate Analysis 59: 272–281.Google Scholar
11.Kochar, S.C. & Xu, M. (2007). Stochastic comparisons of parallel systems when components have PHRs. Probability in the Engineering and Informational Sciences 21: 597–609.Google Scholar
12.Kochar, S.C. & Xu, M. (2010). On the right spread order of convolutions of heterogeneous exponential random variables. Journal of Multivariate Analysis 101: 165–176.Google Scholar
13.Kochar, S.C. & Xu, M. (2011). Stochastic comparisons of spacings from heterogeneous samples. In Wells, M. & Sengupta, A. (eds.), Advances in directional and linear statistics. New York: Springer, pp. 113–129.Google Scholar
14.Marshall, A.W. & Olkin, I. (2007). Life distributions. New York: Springer-Verlag.Google Scholar
15.Marshall, A.W., Olkin, I. and Arnold, B.C. (2011) Inequalities: theory of majorization and its applications, 2nd ed. New York: Springer-Verlag.Google Scholar
16.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
17.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer-Verlag.Google Scholar
18.Zhao, P. & Balakrishnan, N. (2009). Mean residual life order of convolutions of heterogeneous exponential random variables. Journal of Multivariate Analysis 100: 1792–1801.Google Scholar
19.Zhao, P. & Li, X. (2009). Stochastic order of sample range from heterogeneous exponential random variables. Probability in the Engineering and Informational Sciences 23: 17–29.Google Scholar
20.Zhao, P. & Li, X. (2013). On sample range from two heterogeneous exponential variables. In Li, H. & Li, X. (eds.), Lecture notes in statistics, vol. 208. New York: Springer, pp. 125–139.Google Scholar
21.Zhao, P. & Zhang, Y. (2012). On sample ranges in multiple-outlier models. Journal of Multivariate Analysis 111: 335–349.Google Scholar