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Exponential Arctan‐G Family of Distribution With Properties and Applications

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  • Shahid Mohammad
  • Arjun Kumar Gaire

Abstract

Recent research in univariate probability distributions has primarily focused on the introduction of novel generators, families, and additional parameters to existing distributions. The objective is to identify a flexible, valid, and reliable distribution capable of effectively accommodating data across diverse domains. This article introduces a new family of probability distributions called the exponential arctan (ExAT) family. Within this family, a submodel named ExAT − W is formulated using a one‐parameter Weibull distribution as a baseline distribution. The article presents various statistical properties of the proposed distribution, highlighting its unique bimodal hazard rate function. To demonstrate the practical application of the ExAT − W distribution, two examples involving remission times and melanoma data are provided, demonstrating its flexibility, stability, and applicability in real‐world scenarios.

Suggested Citation

  • Shahid Mohammad & Arjun Kumar Gaire, 2025. "Exponential Arctan‐G Family of Distribution With Properties and Applications," Journal of Probability and Statistics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljps:v:2025:y:2025:i:1:n:3643496
    DOI: 10.1155/jpas/3643496
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    References listed on IDEAS

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    1. El-Sayed A. El-Sherpieny & Mamhoud M. Elsehetry, 2019. "Type II Kumaraswamy Half Logistic Family of Distributions with Applications to Exponential Model," Annals of Data Science, Springer, vol. 6(1), pages 1-20, March.
    2. Ibrahim Alkhairy & M. Nagy & Abdisalam Hassan Muse & Eslam Hussam & Sameh S. Askar, 2021. "The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences," Complexity, Hindawi, vol. 2021, pages 1-14, December.
    3. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    4. Hesham Reyad & Mustafa Ç. Korkmaz & Ahmed Z. Afify & G. G. Hamedani & Soha Othman, 2021. "The Fréchet Topp Leone-G Family of Distributions: Properties, Characterizations and Applications," Annals of Data Science, Springer, vol. 8(2), pages 345-366, June.
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