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Sufficient Conditions for some Transform Orders Based on the Quantile Density Ratio

Author

Listed:
  • Antonio Arriaza

    (Universidad de Cádiz, Facultad de Ciencias)

  • Félix Belzunce

    (Departamento Estadística e Investigación Operativa, Universidad de Murcia, Facultad de Matemáticas)

  • Carolina Martínez-Riquelme

    (Departamento Estadística e Investigación Operativa, Universidad de Murcia, Facultad de Matemáticas)

Abstract

In this paper we focus on providing sufficient conditions for some transform orders for which the quantile densities ratio is non-monotone and, therefore, the convex transform order does not hold. These results are interesting for comparing random variables with a non-explicit expression of their quantile functions or they are computationally complex. In addition, the main results are applied to compare two Tukey generalized distributed random variables and to establish new relationships among non-monotone and positive aging notions.

Suggested Citation

  • Antonio Arriaza & Félix Belzunce & Carolina Martínez-Riquelme, 2021. "Sufficient Conditions for some Transform Orders Based on the Quantile Density Ratio," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 29-52, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-019-09740-6
    DOI: 10.1007/s11009-019-09740-6
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    References listed on IDEAS

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    1. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2012. "Comparison of risks based on the expected proportional shortfall," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 292-302.
    2. Alzaid, A. A. & Al-Osh, M., 1989. "Ordering probability distributions by tail behavior," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 185-188, June.
    3. Subhash C. Kochar & Douglas P. Wiens, 1987. "Partial orderings of life distributions with respect to their aging properties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 823-829, December.
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    Cited by:

    1. Félix Belzunce & Carolina Martínez-Riquelme & Magdalena Pereda, 2022. "Sufficient Conditions for Some Stochastic Orders of Discrete Random Variables with Applications in Reliability," Mathematics, MDPI, vol. 10(1), pages 1-15, January.

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