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Preservation of classes of life distributions and stochastic orders under weighting

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  • Bartoszewicz, Jaroslaw
  • Skolimowska, Magdalena

Abstract

In the paper we use a representation of weighted distributions by the Lorenz curve to obtain some results concerning their relations with life distributions. We also consider a problem of preservation of stochastic orderings under weighting. Some extensions of the results of Gupta and Keating [1986. Relations for reliability measures under length biased sampling. Scand. J. Statist. 13, 49-56] and Jain et al. [1989. Relations for reliability measures of weighted distributions. Comm. Statist. Theory Methods 18, 4393-4412] are given.

Suggested Citation

  • Bartoszewicz, Jaroslaw & Skolimowska, Magdalena, 2006. "Preservation of classes of life distributions and stochastic orders under weighting," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 587-596, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:6:p:587-596
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    References listed on IDEAS

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    1. Crescenzo, Antonio Di, 2000. "Some results on the proportional reversed hazards model," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 313-321, December.
    2. Bartoszewicz, Jaroslaw, 2002. "Mixtures of exponential distributions and stochastic orders," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 23-31, March.
    3. Joag-dev, Kumar & Kochar, Subhash & Proschan, Frank, 1995. "A general composition theorem and its applications to certain partial orderings of distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 111-119, February.
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    Cited by:

    1. Navarro, J. & Sunoj, S.M. & Linu, M.N., 2011. "Characterizations of bivariate models using dynamic Kullback-Leibler discrimination measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1594-1598, November.
    2. Bartoszewicz, Jaroslaw, 2009. "On a representation of weighted distributions," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1690-1694, August.
    3. M. Kayid & S. Izadkhah & J. Jarrahiferiz & P. Asghari, 2016. "A mixture model of size-biased distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 513-529, July.
    4. Denuit, Michel, 2019. "Size-biased risk measures of compound sums," LIDAM Discussion Papers ISBA 2019009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Blazej, Pawel, 2008. "Preservation of classes of life distributions under weighting with a general weight function," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3056-3061, December.
    6. Sánchez-Sánchez, M. & Sordo, M.A. & Suárez-Llorens, A. & Gómez-Déniz, E., 2019. "Deriving Robust Bayesian Premiums Under Bands Of Prior Distributions With Applications," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 147-168, January.

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