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Ordering probability distributions by tail behavior

Author

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  • Alzaid, A. A.
  • Al-Osh, M.

Abstract

We introduce, what we call, "the exponent function of a probability distribution" which can be used for ordering probability distributions according to their tail behavior. Some properties of this function as well as the related "failure rate quantile function" are discussed. An ordering among probability distributions based on the right tail exponent of Parzen (1979) is introduced and called "Parzen ordering". Some properties of this ordering along with examples are given.

Suggested Citation

  • Alzaid, A. A. & Al-Osh, M., 1989. "Ordering probability distributions by tail behavior," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 185-188, June.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:2:p:185-188
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    Cited by:

    1. 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.
    2. Idir Arab & Paulo Eduardo Oliveira & Tilo Wiklund, 2021. "Convex transform order of Beta distributions with some consequences," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 238-256, August.

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