Confidence Interval for Parameters Estimates in Circular Simultaneous Functional Relationship Model (CSFRM) for Equal Variances using Normal Asymptotic and Bootstrap Confidence Intervals; [Selang Keyakinan Anggaran Parameter untuk Model Hubungan Fungsian Membulat Serentak (CSFRM) dengan Andaian Ralat Varians sama menggunakan Pendekatan Asimptot dan Pembutstrapan]

• Published in: Sains Malaysiana
• Main Author: Badarisam F.N.; Anuar M.S.M.; Hussin A.G.; Rambli A.; Zulkifli N.R.
• Format: Article
• Language: English
• Published: Penerbit Universiti Kebangsaan Malaysia 2022
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85145953741&doi=10.17576%2fjsm-2022-5111-25&partnerID=40&md5=16bee6ce2e47382bd56a29f464411198

Few studies have considered the functional relationship model for circular variables. Anuar has proposed a new model of Circular Simultaneous Functional Relationship Model for equal variances. However, the confidence interval for all parameter estimates in this model has not received any consideration in any literature. This paper proposes the confidence interval for all parameter estimates of von Mises distribution in this model. The parameters are estimated using minimum sum (ms) and polyroot function provided in (built-in package) Splus statistical software. The parameters confidence may be obtained from parameter estimation. Those estimation values are obtained by minimizing the negative value of the log-likelihood function. Then, the confidence interval for all parameters based on the bootstrap method will be compared with the normal asymptotic confidence interval via simulation studies. It is found that bootstrap method is the superior method by measuring the performance using coverage probability and expected length. The confidence intervals are illustrated using real wind direction data of Bayan Lepas that collected at 16.3 m above ground level, latitude 05°18’N and longitude 100°16’E. The results showed that the estimate parameters fall between the estimate interval, and we note that the method works well for this model. © 2022 Penerbit Universiti Kebangsaan Malaysia. All rights reserved.