A New Hyperbolic Tangent Family of Distributions: Properties and Applications

Shahid Mohammad () and Isabel Mendoza ()
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Shahid Mohammad: University of Wisconsin Oshkosh
Isabel Mendoza: University of Wisconsin Oshkosh

Annals of Data Science, 2025, vol. 12, issue 2, No 2, 457-480

Abstract: Abstract This paper introduces a new family of distributions called the hyperbolic tangent (HT) family. The cumulative distribution function of this model is defined using the standard hyperbolic tangent function. The fundamental properties of the distribution are thoroughly examined and presented. Additionally, an inverse exponential distribution is employed as a sub-model within the HT family, and its properties are also derived. The parameters of the HT family are estimated using the maximum likelihood method, and the performance of these estimators is assessed using a simulation approach. To demonstrate the significance and flexibility of the newly introduced family of distributions, two real data sets are utilized. These data sets serve as practical examples that showcase the applicability and usefulness of the HT family in real-world scenarios. By introducing the HT family, exploring its properties, employing the maximum likelihood estimation, and conducting simulations and real data analyses, this paper contributes to the advancement of statistical modeling and distribution theory.

Keywords: Goodness-of-fit; Hyperbolic tangent function; Inverse exponential distribution; Maximum likelihood estimation; Moments; Simulation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s40745-024-00516-5

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