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Characterizations of the geometric distribution via residual lifetime

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  • Nan-Cheng Su

    (National Taipei University)

  • Wan-Ping Hung

    (National Sun Yet-Sen University)

Abstract

In this work, some characterizations of the geometric distribution based on two kinds of residual lifetime are presented. Firstly we characterize geometric distribution by using certain relationships of moments of the truncated life from below, that is $$\max \{X-t,0\}$$ max { X - t , 0 } , where X is a positive integer-valued random variable. Secondly using certain relationships of moments of residual life $$\gamma _{t}$$ γ t at t of a renewal process, we characterize the common distribution of the inter-arrival times $$ \{X_{i},i\ge 1\}$$ { X i , i ≥ 1 } to be geometrically distributed when $$X_{1}$$ X 1 is also a positive integer-valued random variable.

Suggested Citation

  • Nan-Cheng Su & Wan-Ping Hung, 2018. "Characterizations of the geometric distribution via residual lifetime," Statistical Papers, Springer, vol. 59(1), pages 57-73, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0751-1
    DOI: 10.1007/s00362-016-0751-1
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    References listed on IDEAS

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    1. Ramesh C. Gupta, 2006. "Variance residual life function in reliability studies," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 343-355.
    2. Roy, Dilip & Gupta, R. P., 1999. "Characterizations and model selections through reliability measures in the discrete case," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 197-206, June.
    3. Kumar Kattumannil Sudheesh & N. Unnikrishnan Nair, 2010. "Characterization of discrete distributions by conditional variance," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 77-85.
    4. A. Dallas, 1979. "On the exponential law," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 26(1), pages 105-108, December.
    5. Unnikrishnan Nair, N. & Sankaran, P.G., 2013. "Characterizations of discrete distributions using reliability concepts in reversed time," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1939-1945.
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