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Characterizations based on higher order and partial moments of inactivity time

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Abstract

Due to the important role in theory of reliability, forensic science, study of risk analysis, actuarial science, survival analysis, and many other areas of applied probability, the study of inactivity time and its higher order and partial moments has received considerable attention from many authors. In the present paper we give some further insight on the subject. We provide characterization of some continuous distributions based on higher order moments of inactivity time. It is shown that the distribution function can be obtained uniquely through the higher order moments of inactivity time. Furthermore, we study some characterizations based on partial moments of the inactivity time.

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References

  • Abraham B, Nair NU (2001) On characterizing mixtures of some life distributions. Stat Papers 42:387–393

    Article  MathSciNet  MATH  Google Scholar 

  • Boyce WE, DiPrima RC (1997) Elementary differential equations and boundary value problem. Wiley, New York

    MATH  Google Scholar 

  • Castillo E, Hadi AS (1995) Modeling lifetime data with applications to fatigue models. J Am Stat Assoc 90:1041–1054

    Article  MathSciNet  MATH  Google Scholar 

  • Dallas AC (1979) On the exponential law. Metrika 26:105–108

    Article  MathSciNet  MATH  Google Scholar 

  • Dimaki C, Xekalaki E (1990) Identifiability of income distributions in the context of damage and generating models. Commun Stat 19(8):2757–2766

    Article  MathSciNet  MATH  Google Scholar 

  • El-Arishy S (2005) A conditional variance characterization of some discrete probability distributions. Stat Papers 46:31–45

    Article  MathSciNet  MATH  Google Scholar 

  • Galambos J, Hagwood C (1992) The characterization of a distribution function by the second moment of the residual life. Commun Stat 21(5):1463–1468

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta PL, Gupta RC (1983) On the moments of residual life in reliability and some characterization result. Commun Stat 12(4):449–461

    Article  MathSciNet  MATH  Google Scholar 

  • Huang WJ, Su NC (2012) Characterization of distribution based on moments of residual life. Commun Stat 41:2750–2761

    Article  MathSciNet  MATH  Google Scholar 

  • Kundu C, Nanda AK (2010) Some reliability properties of the inactivity time. Commun Stat 39:899–911

    Article  MathSciNet  MATH  Google Scholar 

  • Lin GD (2003) Characterization of the exponential distribution via the residual lifetime. Sankhy\(\bar{a}\): Ser A 65:249–258

  • Nagaraja HN (1975) Characterization of some diustributions by conditional moments. J Indian Stat Assoc 13:57–61

    Google Scholar 

  • Nair NU, Sankaran PG, Sunoj SM (2013) Quantile based reliability aspects of partial moments. J Korean Stat Soc 42:329–342

    Article  MathSciNet  MATH  Google Scholar 

  • Nanda AK, Singh H, Misra N, Paul P (2003) Reliability properties of reversed residual lifetime. Commun Stat 32(10):2031–2042

    Article  MathSciNet  MATH  Google Scholar 

  • Navarro J, Franco M, Ruiz JM (1998) Characterization through moments of the residual life and condition spacing. Sankhy\(\bar{a}\): Ser A 60:36–48

  • Ruiz JM, Navarro J (1995) Characterization of discrete distributions using expected values. Stat Papers 36:237–252

    Article  MathSciNet  MATH  Google Scholar 

  • Ruiz JM, Navarro J (1996) Characterizations based on conditional expectations of the double truncated distribution. Ann Inst Stat Math 48:563–572

    Article  MATH  Google Scholar 

  • Sankaran PG, Nair NU (2000) On some reliability aspects of Pearson family of distributions. Stat Papers 41:109–117

    Article  MathSciNet  MATH  Google Scholar 

  • Sunoj SM (2004) Characterizations of some continuous distributions using partial moments. Metron LXII(3):353–362

    MathSciNet  Google Scholar 

  • Su JC, Huang WJ (2000) Characterizations based on conditional expectations. Stat Papers 41:423–435

    Article  MathSciNet  MATH  Google Scholar 

  • Sunoj SM, Maya SS (2008) The role of lower partial moments in stochastic modeling. Metron LXVI(2):223–242

    MATH  Google Scholar 

  • Winkler RL, Roodman GM, Britney RR (1972) The determination of partial moments. Manag Sci 19(3):290–296

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors thank the Editor-in-Chief of the journal and anonymous reviewers for their valuable comments and suggestions on the earlier version of the manuscript which lead to considerable improvement in the contents. The financial support (Ref. No. SR/FTP/MS-016/2012) rendered by the Department of Science and Technology, Government of India is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Rajiv Gandhi Institute of Petroleum Technology, Rae Bareli, 229 316, India

    Chanchal Kundu & Kshirod Sarkar

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  1. Chanchal Kundu
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  2. Kshirod Sarkar
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Correspondence to Chanchal Kundu.

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Kundu, C., Sarkar, K. Characterizations based on higher order and partial moments of inactivity time. Stat Papers 58, 607–626 (2017). https://doi.org/10.1007/s00362-015-0714-y

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  • DOI: https://doi.org/10.1007/s00362-015-0714-y

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