Parameter Estimation on Simultaneous Linear Functional Relationship of Melaka Wind Data with Error Terms

Nur Ain Al-Hameefatul Jamaliyatul; Nurkhairany Amyra Mokhtar; Basri Badyalina; Adzhar Rambli; Yong Zulina  Zubairi

Authors

Nur Ain Al-Hameefatul Jamaliyatul Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM) Johor Branch, Segamat Campus, Johor, Malaysia
Nurkhairany Amyra Mokhtar Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM) Johor Branch, Segamat Campus, Johor, Malaysia
Basri Badyalina Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM) Johor Branch, Segamat Campus, Johor, Malaysia
Adzhar Rambli School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Shah Alam, Selangor, Malaysia
Yong Zulina Zubairi Institute of Advanced Studies, Universiti Malaya, Kuala Lumpur, Malaysia

Keywords:

Simultaneous linear functional model, maximum likelihood estimation, environmental data

Abstract

This study extends the parameter estimation from a bivariate linear functional relationship (LFRM) to a simultaneous LFRM designed for multiple linear variables, employing the maximum likelihood estimation (MLE) method. A simulation study was conducted to examine the bias in parameter estimation. The significance of the simultaneous LFRM lies in its ability to explore relationships among multiple linear variables, with particular emphasis on considering error terms for all variables. The study reveals that the estimated parameters exhibit minimal bias. The applicability of this proposed simultaneous model is illustrated using environmental data such as wind speed, temperature, and humidity from Malacca throughout the southwest monsoon for 128 days in 2020.