Estimation of Rayleigh Distribution Parameters Using the Maximum Likelihood Estimation Method on Wind Speed Data in Jayapura

Safitri Rahayu; Agustinus Langowuyo

doi:10.31605/saintifik.v12i2.668

Safitri Rahayu Universitas Cenderawasih
Agustinus Langowuyo Universitas Cenderawasih

DOI: https://doi.org/10.31605/saintifik.v12i2.668

Keywords: Rayleigh Distribution, Wind Speed, Maximum Likelihood Estimation, Kolmogorov-Smirnov, Anderson-Darling, Goodness-of Fit Test

Abstract

This study aims to analyze the characteristics of wind speed data and test its suitability to the Rayleigh distribution using the Maximum Likelihood Estimation (MLE) method. The data used consists of 66 wind speed observations. The analysis begins with descriptive statistics showing an average value of 7.21 km/h, a median of 7.3 km/h, a mode of 4.9 km/h, a variance of 5.73, and a standard deviation of 2.39 km/h. The histogram results show a unimodal distribution pattern with data concentration in the range of 6–9 km/h, while the skewness value of -0.333889 indicates a relatively low negative skew so that the data distribution is still close to symmetrical. The estimation of the Rayleigh distribution parameters using the MLE method produces a scale parameter (σ) value of 5.3702, indicating a fairly large variation in wind speed data. Next, a distribution suitability test was carried out using the Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests. The KS test results produced a statistic of 0.2041 with a p-value of 0.0069, thus rejecting the null hypothesis and declaring the data not to follow the Rayleigh distribution. Conversely, the AD test produced a statistic of 0.5278 with a p-value of 0.1718, thus failing to reject the null hypothesis and declaring the Rayleigh distribution still appropriate for modeling the data. The difference in the results of the two tests is caused by the difference in sensitivity of the methods in detecting distribution deviations. Overall, the Rayleigh distribution can still be used to describe the probability characteristics of wind speed data, although there are some deviations between the theoretical distribution and the actual data.

Downloads

Download data is not yet available.

References

Casella, G., & Berger, R.L. (2002). Statistical Inference (2 nd ed.). Duxbury Press.

Hapsah, S., Somayasa, W., & Mukhtar, N. (2025). Rayleigh Distribution Parameter Estimation on Type II Censored Samples. Bakti Cendekia: National Journal of Multidisciplinary Research Results , 2(1), 145-166.

Johnson, R. A., & Wichern, D. W. (2019). Applied Multivariate Statistical Analysis (7th ed .). Pearson.

Langowuyo, A., Yokhu, S., & Reba, F. (2025). Parameter Estimation and Analysis of Average Years of Schooling in Merauke District with Birnbaum-Saunders Distribution Approach. KUBIK: Jurnal Publikasi Ilmiah Matematika, 10(1), 48-55.

Nocedal, J., & Wright, S. J. (2006). Numerical Optimization ( 2nd ed.). Springer.

Pawitan, Y. (2001). In All Likelihood: Statistical Modeling and Inference Using Likelihood. Oxford University Press.

Simbolon, RU (2021). Estimation of Rayleigh Distribution Parameters Using the Maximum Likelihood Method and the Bayes Method on Type II Sensor Data (Bachelor's Thesis, University of Lampung).

Sroyer, A. M., Tandiangnga, T., Reba, F., & Beno, I. S. (2018). Comparison of Parameter Estimation Methods to Determine the Frequency Data Magnitude of Aftershock in Nabire, Papua. Journal of Science & Science Education, 2(2), 17-21.

Wilks, D. S. (2019). Statistical Methods in the Atmospheric Sciences (4 th ed.). Academic Press.