A Flexible Sine-Transformed Extension of the Nakagami Distribution

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DOI: https://doi.org/10.28924/2291-8639-24-2026-277
Published: Sep 2, 2026
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Parawan Pijitrattana, Ibrahim Abdullahi, A Flexible Sine-Transformed Extension of the Nakagami Distribution, Int. J. Anal. Appl., 24 (2026), 277.

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Parawan Pijitrattana, Ibrahim Abdullahi

Abstract

A central problem in distribution theory is the construction of flexible models that retain analytical tractability while improving shape adaptability in applications. We propose a sine-transformed extension of the Nakagami distribution by applying a trigonometric mapping to the baseline cumulative distribution function. The resulting sine-transformed Nakagami model preserves the original two-parameter structure, admits closed-form expressions for both the distribution and density functions, and yields tractable reliability measures. We establish key structural properties, including validity, smoothness, and well-defined support; in addition, a hazard modulation representation relative to the classical Nakagami model is derived; and obtain explicit upper-tail asymptotics showing that the proposed transformation preserves the light-tailed class while modifying survival decay in a controlled and interpretable manner. Series representations are developed to facilitate the computation of moments and other related functionals. Parameters are estimated by maximum likelihood using numerical optimization, and finite-sample performance is evaluated through Monte Carlo simulation studies. Applications to real data illustrate that the sine-transformed Nakagami distribution provides an improved goodness of fit compared with the classical Nakagami model for reliability-type data.

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