# Modelling Wind Speed, Humidity, and Temperature in Butterworth and Melaka during Southwest Monsoon in 2020 with a Simultaneous Linear Functional Relationship

## Authors

• Nur Ain Al-Hameefatul Jamaliyatul Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM), Johor Branch, Segamat Campus, Segamat, Johor, Malaysia
• Nurkhairany Amyra Mokhtar Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM), Johor Branch, Segamat Campus, Segamat, Johor, Malaysia
• Basri Badyalina Mathematical Sciences Studies, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM), Johor Branch, Segamat Campus, Segamat, 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 Relationship Model, Fisher Information Matrix, Maximum Likelihood Estimation, Linear Variables

## Abstract

The extension of parameter estimation from a bivariate linear functional relationship model (LFRM) to simultaneous LFRM for linear variables using the maximum likelihood estimation (MLE) method is explored in this paper. The covariance matrix of the parameter estimates is derived through the Fisher information matrix. A simulation study was done to investigate the performance of the parameter estimation. According to the simulation study, the estimated parameters have a small bias. The beauty of simultaneous LFRM lies in developing the model to study the relationship between more than two linear variables while considering error terms for all variables. The applicability of the proposed simultaneous model is demonstrated using wind speed, humidity, and temperature data from Butterworth and Melaka during the southwest monsoon season of 2020.

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