This paper proposes GL-moments’ method as a generalization to the TL-moments and the L-moments methods. Population GL-moments in terms of the quantile function and shifted Jacobi polynomials were defined. Some relations between GL-moments depending on Jacobi Polynomials were also derived. Furthermore, interpretation of the first two population GL-moments by U-statistics was introduced. Also, we obtained two expressions to estimate the population GL-moments: the first expression, which depends on Downton’s estimator, is a nearly unbiased estimator. Finally, to avoid an upper control limit exceeding one in p-chart, we propose a control chart based on generalized linear moments for monitoring fractional, rates and proportions data. Control limits are proposed and simulated average run length experiments show the proposed control charts to be less influenced by extreme observations than their classical counterparts and lead to tighter control limits. An example is given that summarizes the benefits included in the charts.
M. Abd Elrazik, Enayat and M. Mansour, Mahmoud
"On Generalize L-moments Method and Application on Control Chart for Monitoring Fractional, Rates and Proportions Data,"
Information Sciences Letters: Vol. 11
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Available at: https://digitalcommons.aaru.edu.jo/isl/vol11/iss1/13