The development of new crescent moon visibility criteria using circular regression model / Zuhaili Mohd Nasir - Zuhaili , Mohd Nasir (2021)
The lunar crescent moon visibility has a long research history since Babylonian Era. It is important in determining the local Islamic calendar and setting the dates of important Islamic events. The possible visibility of the crescent moon is dependent on a few criteria used during the sighting process. The methods to determine minimum condition or criteria for crescent moon visibility based on the linear statistical theory that have so far been developed are not that suitable for this study because the useful variables are in the circular unit. Thus, new visibility tests are proposed in this research using the circular regression model, which will divide the data into three visibility categories; visible to the unaided eye, may need optical aid and not visible. Using the residuals of the fitted circular regression model, we formulate the method for separating the categories. We apply the model on 254 observations collected at Baitul Hilal Teluk Kemang Malaysia, starting from March 2000 to June 2019. Based on the analysis, the visibility test developed based on the elongation of the moon (dependent variable) and altitude of the moon (independent variable) gives the smallest rate of misclassification. From the statistical analysis, we propose the elongation of 7.28°, the altitude of the moon of 3.39° and the arc of vision of 3.74° at sunset as the new crescent visibility criteria. The new criteria have a significant impact on improving the chance of observing the crescent moon and hence producing a more accurate Islamic calendar in Malaysia.