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Some New Results Related to the Likelihood Ratio and the Laplace Transform Ordering

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  • Abdulaziz Alenazi

    (Department of Mathematics, College of Science, Northern Border University, Arar 91431, Saudi Arabia
    Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia)

Abstract

The purpose of this paper is twofold. First, we aim to study some new properties and relations for the likelihood ratio order. In particular, we present new integral inequalities involving the ratio of two probability density functions and the ratio of two corresponding cumulative distribution functions. Specifically, we provide alternative proofs for certain relationships between the likelihood ratio order and other stochastic orders. Second, we consider the Laplace ratio order and present new characterizations for the Laplace ratio ordering of two random variables. These results contribute to the literature on stochastic orders by providing new characterizations and inequalities that can be useful in probability theory, risk analysis and reliability theory.

Suggested Citation

  • Abdulaziz Alenazi, 2025. "Some New Results Related to the Likelihood Ratio and the Laplace Transform Ordering," Mathematics, MDPI, vol. 13(12), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1989-:d:1680328
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    References listed on IDEAS

    as
    1. Bartoszewicz, Jaroslaw, 1999. "Characterizations of stochastic orders based on ratios of Laplace transforms," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 207-212, April.
    2. Bartoszewicz, Jaroslaw, 2000. "Stochastic orders based on the Laplace transform and infinitely divisible distributions," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 121-129, November.
    3. Denuit, Michel, 2001. "Laplace transform ordering of actuarial quantities," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 83-102, August.
    4. Fatemeh Gharari & Masoud Ganji, 2023. "A new stochastic order based on discrete Laplace transform and some ordering results of the order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(6), pages 1963-1980, March.
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