In this paper, three objective functions of M-estimates (Huber, Hampel, and Bisquare) are used in order to obtain robust estimates of the gamma distribution parameters, and then compare its estimates with estimates provided by the common conventional methods (moment estimators, maximum-likelihood estimators and method of maximum product spacings), to determine the most appropriate methods for estimating the parameters of gamma distribution, by applying the previous methods to real data as well as to generated data, both of which contain different percentages of outliers. Monte Carlo simulation was used to perform the numerical comparison. The simulation results confirmed that the M-estimates give more accurate and higher efficiency estimations when estimating the gamma distribution parameter. It was concluded that the most suitable method for estimating the gamma distribution parameters is the M- estimation method with its three objective functions (Huber, Hampel, and Bisquare), for small and large samples especially in the presence of outliers, and its estimates, in this case, are characterized by greater accuracy and higher efficiency. It was also concluded that the best estimate of robust M-estimation, in this case, is Bisquare method.
Agamy, Mohamed Abdelsalam, & Khmar, Ezzat Hussein. (2023). Modern Robust M-Estimation of the Gamma Distribution with Extreme Observations. المجلة العلمية للدراسات والبحوث المالية والتجارية, 4(2), 621-641. doi: 10.21608/cfdj.2023.289023
MLA
Mohamed Abdelsalam Agamy; Ezzat Hussein Khmar. "Modern Robust M-Estimation of the Gamma Distribution with Extreme Observations". المجلة العلمية للدراسات والبحوث المالية والتجارية, 4, 2, 2023, 621-641. doi: 10.21608/cfdj.2023.289023
HARVARD
Agamy, Mohamed Abdelsalam, Khmar, Ezzat Hussein. (2023). 'Modern Robust M-Estimation of the Gamma Distribution with Extreme Observations', المجلة العلمية للدراسات والبحوث المالية والتجارية, 4(2), pp. 621-641. doi: 10.21608/cfdj.2023.289023
VANCOUVER
Agamy, Mohamed Abdelsalam, Khmar, Ezzat Hussein. Modern Robust M-Estimation of the Gamma Distribution with Extreme Observations. المجلة العلمية للدراسات والبحوث المالية والتجارية, 2023; 4(2): 621-641. doi: 10.21608/cfdj.2023.289023
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