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.
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Acknowledgements
The authors want to acknowledge the comments by an anonymous referee that have greatly improved the presentation and the contents of this paper. We also want to thank Joseph Hooly for his help to improve this paper language-wise. Félix Belzunce and Carolina Martínez-Riquelme want to acknowledge the support received by the Ministerio de Economía, Industria y Competitividad under grant MTM2016-79943-P (AEI/FEDER, UE) and Antonio Arriaza acknowledges the support received by the Ministerio de Economía y Competitividad under grant MTM2017-89577-P.
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Arriaza, A., Belzunce, F. & Martínez-Riquelme, C. Sufficient Conditions for some Transform Orders Based on the Quantile Density Ratio. Methodol Comput Appl Probab 23, 29–52 (2021). https://doi.org/10.1007/s11009-019-09740-6
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DOI: https://doi.org/10.1007/s11009-019-09740-6