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Monotonicity results and new bounds for the Mills ratio

Author

Listed:
  • Zhen-Hang Yang

    (State Grid Zhejiang Electric Power Company Research Institute)

  • Jing-Feng Tian

    (North China Electric Power University)

Abstract

The Mills ratio of the standard Gaussian law plays an important role in probability and statistics since its reciprocal is the failure rate function. In the paper, we verify the increasing property of the Turán-type ratio of the higher derivative of the Mills ratio. This result yields two new bounds for the Mills ratio (or failure rate function) having several interesting properties, and improves known results.

Suggested Citation

  • Zhen-Hang Yang & Jing-Feng Tian, 2025. "Monotonicity results and new bounds for the Mills ratio," Statistical Papers, Springer, vol. 66(1), pages 1-27, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01646-x
    DOI: 10.1007/s00362-024-01646-x
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    References listed on IDEAS

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    1. Masoud Faridi & Majid Jafari Khaledi, 2022. "The polar-generalized normal distribution: properties, Bayesian estimation and applications," Statistical Papers, Springer, vol. 63(2), pages 571-603, April.
    2. Ping Sun & Ze-Chun Hu & Wei Sun, 2024. "Variation comparison between infinitely divisible distributions and the normal distribution," Statistical Papers, Springer, vol. 65(7), pages 4405-4429, September.
    3. Tommaso Lando, 2022. "Testing convexity of the generalised hazard function," Statistical Papers, Springer, vol. 63(4), pages 1271-1289, August.
    4. Tommaso Lando, 2022. "Correction to: Testing convexity of the generalised hazard function," Statistical Papers, Springer, vol. 63(4), pages 1291-1293, August.
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