article · Alexandria Engineering Journal
A new statistical distribution family has been developed using a mathematical framework based on the hyperbolic sine function. Using the traditional Rayleigh distribution as a baseline, the resulting model is termed the new hyperbolic Sine-Rayleigh distribution. Structural characteristics of this novel distribution were analysed, and the behaviours of its underlying distributional functions were mapped. To calibrate the model, researchers applied the maximum likelihood estimation technique to estimate the necessary distribution parameters. The performance and accuracy of these estimators were evaluated through a simulation study. In addition, the practical value and efficacy of the proposed model were tested against realistic data sets drawn from engineering science, demonstrating its capacity to describe physical data.
Accurate statistical models help engineers understand uncertainty, risk, and variability in complex systems. By introducing a flexible distribution based on the hyperbolic sine function, this research provides analysts with an enhanced mathematical tool to model real-world observations that standard distributions might struggle to capture, improving the precision of engineering simulations.
The model offers utility for data analysts and reliability engineers working on industrial simulation and predictive maintenance. While validated using realistic engineering datasets, this remains early-stage applied research. Direct commercialisation would require the distribution to be implemented within commercial statistical software suites or proprietary industrial analytics tools used in engineering design.
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This study focuses on a novel family of distributions inspired by the hyperbolic sine function. The Rayleigh distribution is the base model for the newly formed family of distributions known as the new hyperbolic Sine-Rayleigh distribution. The recommended distribution’s distinct structural traits have been examined. The behaviors of the distributional functions of the proposed model are depicted in several figures. The maximum likelihood estimation procedure is employed to estimate the specified distribution parameters. A simulation study was carried out to examine and evaluate the behavior of the estimators. Moreover, the efficacy of the specified distribution is supported by realistic data sets pertaining to engineering science.
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DOI: 10.1016/j.aej.2023.04.048
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