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Estimation of Reliability in Multicomponent Stress-Strength Based on Dagum Distribution

Author

Listed:
  • Fulment Arnold K.
  • Josephat Peter K.

    (Department of Statistics, School of Mathematical Sciences, The University of Dodoma, P.O. Box 338, Dodoma, Tanzania)

  • Srinivasa Rao Gadde

    (Department of Statistics, School of Mathematical Sciences, The University of Dodoma, P.O. Box 338, Dodoma, Tanzania)

Abstract

We consider the Dagum distribution for estimating the reliability of a k-component stress-strength system with different shape values of the shape parameter. We assume that the system has strength modelled by k independent and identically distributed random variables, and each system’s component experiences random stress. We construct maximum likelihood estimators for the system’s reliability and study their asymptotic properties. We evaluate the small sample performance of the estimators through Monte Carlo simulation. Finally, we illustrate the procedure using real data.

Suggested Citation

  • Fulment Arnold K. & Josephat Peter K. & Srinivasa Rao Gadde, 2017. "Estimation of Reliability in Multicomponent Stress-Strength Based on Dagum Distribution," Stochastics and Quality Control, De Gruyter, vol. 32(2), pages 77-85, December.
    • Handle: RePEc:bpj:ecqcon:v:32:y:2017:i:2:p:77-85:n:1
    DOI: 10.1515/eqc-2017-0009
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    References listed on IDEAS

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    1. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    2. Filippo Domma & Sabrina Giordano & Mariangela Zenga, 2009. "The Fisher Information Matrix In Doubly Censored Data From The Dagum Distribution," Working Papers 200908, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    3. G. Srinivasa Rao & Muhammad Aslam & Debasis Kundu, 2015. "Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4953-4961, December.
    4. Filippo Domma & Sabrina Giordano & Mariangela Zenga, 2011. "The Fisher Information Matrix in Right Censored Data from the Dagum Distribution," Working Papers 201104, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    5. Claudio Quintano & Antonella D'Agostino, 2006. "Studying Inequality In Income Distribution Of Single‐Person Households In Four Developed Countries," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 52(4), pages 525-546, December.
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