Bivariate Conditional Wigner Semicircle Distribution Modeling of Wind ‎Speed and Direction

Authors

  • Onoghojobi Benson

    Department of Statistics, Federal University Lokoja, Nigeria

  • Otaru Olawale Paul

    Department of Statistics, Federal University Lokoja, Nigeria https://orcid.org/0000-0002-9894-2842

  • David Ibitayo Lanlege

    Department of Mathematics, Federal University Lokoja‎, Nigeria

  • Job Eunice Ohunene

    Department of Statistics, Federal University Lokoja, Nigeria

  • Eseyin Babatunde Olamide

    Department of Statistics, Federal University Lokoja, Nigeria

  • Owonipa Oluremi Rasheedat

    Department of Statistics, Kogi State University, Nigeria

Received date: June 9, 2025

Accepted date: July 1, 2025

Published date: July 6, 2025

DOI:

https://doi.org/10.14419/eqwqbd48

Keywords:

Wigner-Semicircle; Conditional; Marginal; Distribution; Moment; Bivariate; Circular-Variable

Abstract

Wind direction and speed are increasingly significant for societal and human advancement, as it ‎is essential to comprehending and forecasting various events. Therefore, a model that captures ‎the distinct features of wind direction and speed is developed. The conditional and marginal ‎Wigner semicircle distributions were combined to create a bivariate conditional Wigner semicircle ‎distribution. The joint characteristics and estimation of its parameters were determined. Real-world wind speed and direction data, where the conditional reliance and circularity of the ‎variables are suspected, were used to test the model. Based on the goodness-of-fit test and root ‎mean square error, the outcome demonstrates that the model and the data are compatible. The ‎model is suggested for use in situations where consideration must be given to variables with a ‎conditional structure and cyclicity.

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Received date: June 9, 2025

Accepted date: July 1, 2025

Published date: July 6, 2025