Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T06:07:28.128Z Has data issue: false hasContentIssue false
  • English
  • Français

Some stochastic comparisons of lower records and lower record spacings

Published online by Cambridge University Press:  26 January 2022

Narayanaswamy Balakrishnan ,
Antonia Castaño-Martínez  and
Miguel A. Sordo Open the ORCID record for Miguel A. Sordo [Opens in a new window]
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Canada
Antonia Castaño-Martínez
Affiliation:
Department of Statistics and Operations Research, University of Cádiz, Cádiz, Spain
Miguel A. Sordo
Affiliation:
Department of Statistics and Operations Research, University of Cádiz, Cádiz, Spain. E-mail: mangel.sordo@uca.es
Get access Rights & Permissions [Opens in a new window]

Abstract

We obtain here sufficient conditions for increasing concave order and location independent more riskier order of lower record values based on stochastic comparisons of minimum order statistics. We further discuss stochastic orderings of lower record spacings. In particular, we show that increasing convex order of adjacent spacings between minimum order statistics is a sufficient condition for increasing convex order of adjacent spacings of their lower records.

Keywords

Increasing concave orderLocation independent riskier orderLower record spacingsLower record valuesOrder statistics
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 192 - 205
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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

Ahmadi, J. & Arghami, N.R. (2001). Some univariate stochastic orders on record values. Communications in Statistics – Theory and Methods 30: 69–74.CrossRefGoogle Scholar
Ahsanullah, M. (1995). Record statistics. New York: Nova Science Publishers.Google Scholar
Arnold, B.C., Balakrishnan, N., & Nagaraja, H.N. (1992). A first course in order statistics. New York: John Wiley & Sons.Google Scholar
Arnold, B.C., Balakrishnan, N., & Nagaraja, H.N. (1998). Records. New York: John Wiley & Sons.CrossRefGoogle Scholar
Arriaza, A. & Sordo, M.A. (2021). Preservation of some stochastic orders by distortion functions with application to coherent systems with exchangeable components. Applied Stochastic Models in Business and Industry 37: 303–317.CrossRefGoogle Scholar
Arriaza, A., Sordo, M.A., & Suárez-Llorens, A. (2017). Comparing residual lives and inactivity times by transform stochastic orders. IEEE Transactions on Reliability 66: 366–372.CrossRefGoogle Scholar
Balakrishnan, N. & Mi, J. (2001). Order-preserving properties of maximum likelihood estimator. Journal of Statistical Planning and Inference 98: 89–99.CrossRefGoogle Scholar
Balakrishnan, N. & Rao, C.R. (Eds.) (1998). Handbook of statistics 16-order statistics: Theory and methods. Amsterdam: Elsevier.Google Scholar
Balakrishnan, N. & Rao, C.R. (Eds.) (1998). Handbook of statistics 17-order statistics: Applications. Amsterdam: Elsevier.Google Scholar
Balakrishnan, N., Brain, C., & Mi, J. (2002). Stochastic order and MLE of the mean of the exponential distribution. Methodology and Computing in Applied Probability 4: 83–93.CrossRefGoogle Scholar
Balakrishnan, N., Belzunce, F., Sordo, M.A., & Suárez-Llorens, A. (2012). Increasing directionally convex orderings of random vectors having the same copula and their use in comparing ordered data. Journal of Multivariate Analysis 105: 45–54.CrossRefGoogle Scholar
Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt, Rinehart and Winston.Google Scholar
Belzunce, F. (1999). On a characterization of right spread order by the increasing convex order. Statistics & Probability Letters 45: 103–110.CrossRefGoogle Scholar
Belzunce, F., Hu, T., & Khaledi, B.-E. (2003). Dispersion-type variability orders. Probability in the Engineering and Informational Sciences 17: 305–334.CrossRefGoogle Scholar
Belzunce, F., Mercader, A., & Ruiz, J.M. (2005). Stochastic comparisons of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 99–120.CrossRefGoogle Scholar
Belzunce, F., Lillo, R.E., Ruiz, J.M., & Shaked, M. (2007). Stochastic ordering of record and inter-record values. In M. Ahsanullah and M. Raqab (eds.), Recent developments in ordered random variables. New York: Nova Science Publishers, pp. 119–137.Google Scholar
Belzunce, F., Martínez-Riquelme, C., & Mulero, J. (2016). An introduction to stochastic orders. Amsterdam: Elsevier.Google Scholar
Belzunce, F., Martínez-Riquelme, C., Ruiz, J.M., & Sordo, M.A. (2016). On sufficient conditions for the comparison in the excess wealth order and spacings. Journal of Applied Probability 53: 33–46.CrossRefGoogle Scholar
Belzunce, F., Martínez-Riquelme, C., Ruiz, J.M., & Sordo, M.A. (2017). On the comparison of relative spacings with applications. Methodology and Computing in Applied Probability 19: 357–376.CrossRefGoogle Scholar
Castaño-Martínez, A., Pigueiras, G., Psarrakos, G., & Sordo, M.A. (2020). Increasing concave orderings of linear combinations of order statistics with applications to social welfare. Metrika 83: 699–712.CrossRefGoogle Scholar
Castaño-Martínez, A., Pigueiras, G., & Sordo, M.A. (2021). On the increasing convex order of relative spacings of order statistics. Mathematics 9: 618.CrossRefGoogle Scholar
Charalambides, Ch.A. (2007). On the distribution and moments of record values in increasing populations. Journal of the Iranian Statistical Society (JIRSS) 6: 47–60.Google Scholar
David, H.A. & Nagaraja, H.N. (2003). Order statistics, 3rd ed. Hoboken, NJ: John Wiley & Sons.CrossRefGoogle Scholar
Hu, T. & Zhuang, W. (2006). Stochastic orderings between p-spacings of generalized order statistics from two samples. Probability in the Engineering and Informational Sciences 20: 465–479.CrossRefGoogle Scholar
Jewitt, I. (1989). Choosing between risky prospects: The characterization of comparative statics results, and location independent risk. Management Science 35: 60–70.CrossRefGoogle Scholar
Khaledi, B-E. & Shojaei, S.R. (2007). On stochastic orderings between residual record values. Statistics & Probability Letters 77: 1467–1472.CrossRefGoogle Scholar
Khaledi, B.-E., Amiripour, F., Hu, T., & Shojaei, S.R. (2009). Some new results on stochastic comparisons of record values. Communications in Statistics – Theory and Methods 38: 2056–2066.CrossRefGoogle Scholar
Kochar, S.C. (1990). Some partial ordering results on record values. Communications in Statistics – Theory and Methods 19: 299–306.CrossRefGoogle Scholar
Kochar, S.C. (1996). A note on dispersive ordering of record values. Calcutta Statistical Association Bulletin 46: 63–67.CrossRefGoogle Scholar
Kochar, S.C., Li, X., & Shaked, M. (2002). The total time on test transform and the excess wealth stochastic orders of distributions. Advances in Applied Probability 34: 826–845.CrossRefGoogle Scholar
Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. Chichester: John Wiley & Sons.Google Scholar
Nevzorov, V.B. (2001). Records: Mathematical theory. Providence, RI: American Mathematical Society.Google Scholar
Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer-Verlag.CrossRefGoogle Scholar
Shaked, M., Sordo, M.A., & Suárez-Llorens, A. (2010). A class of location-independent variability order with applications. Journal of Applied Probability 47: 407–425.CrossRefGoogle Scholar
Sordo, M.A. (2008). Characterizations of classes of risk measures by dispersive orders. Insurance: Mathematics and Economics 42: 1028–1034.Google Scholar
Sordo, M.A. (2009). On the relationship of location-independent riskier order to the usual stochastic order. Statistics & Probability Letters 79: 155–157.CrossRefGoogle Scholar
Zhao, P. & Balakrishnan, N. (2009). Stochastic comparison and monotonicity of inactive record values. Statistics & Probability Letters 79: 566–572.CrossRefGoogle Scholar
Zhao, P., Li, X., Li, Z., & Xu, M. (2008). Stochastic comparisons of spacings of record values from one or two sample sequences. Statistics 42: 167–177.CrossRefGoogle Scholar
Zhuang, W. & Hu, T. (2009). Multivariate dispersive ordering of spacings of generalized order statistics. Applied Mathematics Letters 22: 968–974.CrossRefGoogle Scholar