Advances and Applications in Statistics
Volume 59, Issue 2, Pages 173 - 197
(December 2019) http://dx.doi.org/10.17654/AS059020173 |
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THE EFFECT OF INTRODUCING A SCALE PARAMETER ON THE ESTIMATION OF OFFSET NORMAL DISTRIBUTION
Amani A. Ahmed, Alyaa R. Zahran, Moshira A. Ismail and Abd El Naser Saad
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Abstract: Directional data in two dimensions are known as circular data. The offset normal distribution, which is a special case of general projected normal distribution, is a symmetric distribution family that is widely used for modeling circular data. It is constructed by projection of bivariate normal distribution (assuming identity variance-covariance matrix, I) onto the unit circle. In this study, we consider the problem of estimating the offset normal distribution with variance-covariance matrix Important circular measures such as angular mean direction and mean resultant length are derived for that case. The study considers two estimation methods: maximum likelihood estimation (using EM-algorithm and Newton-Raphson method) and method of moments estimation. The results show that the performance of the estimators is highly affected with the existence of and the corresponding level of variability. Although the method of moments estimation is easier in calculations but it does not have good performance with large The EM algorithm is easier in calculations and faster in convergence. It gives the best consistent estimators for most scenarios. |
Keywords and phrases: general projected normal distribution, angular mean direction, mean resultant length, moments estimation, maximum likelihood estimation
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