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On the relationship between the reversed hazard rate and elasticity

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Abstract

Despite hazard and reversed hazard rates sharing a number of similar aspects, reversed hazard functions are far less frequently used. Understanding their meaning is not a simple task. The aim of this paper is to expand the usefulness of the reversed hazard function by relating it to other well-known concepts broadly used in economics: (linear or cumulative) rates of increase and elasticity. This will make it possible (i) to improve our understanding of the consequences of using a particular distribution and, in certain cases, (ii) to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way, thus providing a means to achieving distributions that would otherwise be hardly imaginable or justifiable.

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References

  • Badía FG, Berrade MD (2008) On the reversed hazard rate and mean inactivity time of mixtures. In: Bedford T, Quigley J, Walls L, Alkali B, Daneshkhah A, Hardman G (eds) Advances in mathematical modeling for reliability. IOS Press, Amsterdam, pp 103–110

    Google Scholar 

  • Block HW, Savits TH, Singh H (1998) The reversed hazard rate function. Prob Eng Inf Sci 12: 69–90

    Article  MATH  MathSciNet  Google Scholar 

  • Case KE, Fair RC (2007) Principles of economics, 8th edn. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Chandra NK, Roy D (2001) Some results on reverse hazard rate. Prob Eng Inf Sci 15: 95–102

    Article  MATH  MathSciNet  Google Scholar 

  • Chechile RA (2011) Properties of reverse hazard functions. J Math Psychol 55(3): 203–222

    Article  MATH  MathSciNet  Google Scholar 

  • Cheng DW, Zhu Y (1993) Optimal order of servers in a tandem queue with general blocking. Queueing Syst 14(3–4): 427–437

    Article  MATH  MathSciNet  Google Scholar 

  • Chiang AC, Wainwright K (2005) Fundamental methods of mathematical economics, 4th edn. McGraw-Hill, New York

    Google Scholar 

  • Desai D, Mariappan V, Sakhardande M (2011) Nature of reversed hazard rate: an investigation. Int J Performabil Eng 7(2): 165–171

    Google Scholar 

  • Finkelstein MS (2002) On the reversed hazard rate. Reliab Eng Syst Saf 78(1): 71–75

    Article  Google Scholar 

  • Gross ST, Huber-Carol C (1992) Regression models for truncated survival data. Scand J Stat 19: 193–213

    MATH  MathSciNet  Google Scholar 

  • Gupta RD, Gupta RC, Sankaran PG (2004) Some characterization results based on factorization of the (reversed) hazard rate function. Commun Stat Theory Methods 33(12): 3009–3031

    Article  MATH  MathSciNet  Google Scholar 

  • Kalbfleisch JD, Lawless JF (1991) Regression models for right truncated data with applications to AIDS incubation times and reporting lags. Statistica Sinica 1: 19–32

    MATH  Google Scholar 

  • Kijima M (1998) Hazard rate and reversed hazard rate monotonicities in continuous time Markov chains. J Appl Prob 35: 545–556

    Article  MATH  MathSciNet  Google Scholar 

  • Klein JP, Moeschberger ML (2005) Survival analysis: techniques for censored data. Springer, New York

    Google Scholar 

  • Poursaeed MH (2010) A note on the mean past and the mean residual life of a (n−k + 1)-out-of-n system under multi monitoring. Stat Papers 51: 409–419

    Article  MATH  MathSciNet  Google Scholar 

  • Razmkhah M, Morabbi H, Ahmadi J (2012) Comparing two sampling schemes based on entropy of record statistics. Stat Papers 53: 95–106

    Article  MATH  MathSciNet  Google Scholar 

  • Shaked M, Shanthikumar JG (2006) Stochastic orders. Springer, New York

    Google Scholar 

  • Steffensen JF (1930) Some recent researches in the theory of statistics and actuarial science. Cambridge University Press, New York

    Google Scholar 

  • Townsend JT, Wenger MJ (2004) A theory of interactive parallel processing: newcapacity measures and predictions for a response time inequality series. Psychol Rev 111: 1003–1035

    Article  Google Scholar 

  • Xie M, Gaudoin O, Bracquemond C (2002) Redefining failure rate function for discrete distributions. Int J Reliab, Qual Saf Eng 9(3): 275–285

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Applied Economics, Facultad de Economía, Universitat de Valencia, Campus Els Tarongers, 46022, Valencia, Spain

    Ernesto J. Veres-Ferrer & Jose M. Pavía

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  1. Ernesto J. Veres-Ferrer
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  2. Jose M. Pavía
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Correspondence to Jose M. Pavía.

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Veres-Ferrer, E.J., Pavía, J.M. On the relationship between the reversed hazard rate and elasticity. Stat Papers 55, 275–284 (2014). https://doi.org/10.1007/s00362-012-0470-1

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  • DOI: https://doi.org/10.1007/s00362-012-0470-1

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