Skip to main content
Log in

On the Comparison of Relative Spacings with Applications

  • Published:
Methodology and Computing in Applied Probability Aims and scope Submit manuscript

Abstract

In this paper we introduce the notion of relative spacings. We show the interest of this notion in several contexts like reliability and economy, and we provide several results for the comparison of relative spacings from two populations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ascher H, Feingold H (1984) Repairable systems reliability. modeling, inference, misconceptions and their causes. Lecture Notes in Statistics, 7. Marcel Dekker, Inc., New York

    MATH  Google Scholar 

  • Balakrishnan N, Belzunce F, Sordo MA, Suárez-Lloréns A (2011) Increasing directionally convex orderings of random vectors having the same copula and their use in comparing ordered data. J Multivar Anal 105:45–54

    Article  MathSciNet  MATH  Google Scholar 

  • Bandourian R, McDonald JB, Turley RS (2003) A comparison of parametric models of income distribution across countries and over time. Estadística 55:127–142

    MathSciNet  Google Scholar 

  • Barlow RE, Proschan F (1975) Statistical theory of reliability and life testing. Holt, Rinehart and Winston, New York

    MATH  Google Scholar 

  • Belzunce F, Lillo R, Ruiz JM, Shaked M (2001) Stochastic comparisons of nonhomogeneous processes. Probab Eng Inf Sci 15:199–224

    Article  MathSciNet  MATH  Google Scholar 

  • Belzunce F, Martínez-Riquelme C, Ruiz JM, Sordo MA (2016) On sufficient conditions for the comparison in the excess wealth order and spacings. J Appl Probab. to appear

  • Belzunce F, Mercader JA, Ruiz JM (2005) Stochastic comparisons of generalized order statistics. Probab Eng Inf Sci 19:99–120

    Article  MathSciNet  MATH  Google Scholar 

  • Belzunce F, Pinar JF, Ruiz JM, Sordo MA (2012) Comparisons of risks based on the expected proportional shortfall. Insur Math Econ 51:292–302

    Article  MathSciNet  MATH  Google Scholar 

  • Belzunce F, Pinar JF, Ruiz JM, Sordo MA (2013) Comparison of concentration for several families of income distributions. Stat Probab Lett 83:1036–1045

    Article  MathSciNet  MATH  Google Scholar 

  • Chakravarty SR, Moyes P (2003) Individual welfare, social deprivation and income taxation. Econ Theory 21:843–869

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta RC, Kirmani SNUA (1988) Closure and monotonicity properties of nonhomogeneous Poisson processes and record values. Probab Eng Inf Sci 2:475–484

    Article  MATH  Google Scholar 

  • Kamps U (1995a) A concept of generalized order statistics. Teubner, Stuttgart

    Book  MATH  Google Scholar 

  • Kamps U (1995b) A concept of generalized order statistics. J Stat Plan Infer 48:1–23

    Article  MathSciNet  MATH  Google Scholar 

  • Kirmani SNUA, Gupta RC (1992) Some moment inequalities for the minimal repair process. Probab Eng Inf Sci 6:245–255

    Article  MATH  Google Scholar 

  • Kochar SC (1990) Some partial ordering results on record values. Commun Stat Theory Methods 19:299–306

    Article  MathSciNet  MATH  Google Scholar 

  • Kochar SC (1996a) Some results on interarrival times of nonhomogeneous Poisson processes. Probab Eng Inf Sci 10:75–85

    Article  MathSciNet  MATH  Google Scholar 

  • Kochar SC (1996b) A note on dispersive ordering of record values. Calcutta Stat Assoc Bull 46:63–67

    MathSciNet  MATH  Google Scholar 

  • Lai CD, Xie M (2006) Stochastic ageing and dependence for reliability. Springer, New York

    MATH  Google Scholar 

  • McDonald JB (1984) Some generalized functions for the size distribution of income. Econometrica 52:647–663

    Article  MATH  Google Scholar 

  • Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley Series in Probability and Statistics, Chichester

    MATH  Google Scholar 

  • Oliveira PE, Torrado N (2015) On proportional reversed failure rate class. Stat Papers 56:999–1013

    Article  MathSciNet  MATH  Google Scholar 

  • Ramos HM, Sordo MA (2001) The proportional likelihood ratio and applications. Qüestiió 25:211–223

    MathSciNet  MATH  Google Scholar 

  • Runciman WG (1966) Relative deprivation and social justice. Routledge and Kegan Paul, London

    Google Scholar 

  • Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York

    Book  MATH  Google Scholar 

  • Torrado N., Lillo R. E. (2013). In: Li H, Li X (eds) On stochastic properties of spacings with applications in multiple-outlier models. Springer, New York, pp 103–123

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Félix Belzunce.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belzunce, F., Martínez-Riquelme, C., Ruiz, J.M. et al. On the Comparison of Relative Spacings with Applications. Methodol Comput Appl Probab 19, 357–376 (2017). https://doi.org/10.1007/s11009-016-9479-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11009-016-9479-6

Keywords

Mathematics Subject Classification (2010)

Navigation