On Designing EWMA Charts to Model Demographic Trends with Generalized Extreme Value Distribution

Abdur Rahman, King Fahd University of Petroleum and Minerals

Co-authors: Nasir Abbas, King Fahd University of Petroleum and Minerals

Abstract: Demography and policy rely on monitoring life course events such as fertility and mortality rates in various countries. The most used measure to determine whether a nation is replacing its population is the total fertility rate(TFR). In contrast, crude death rate (CDR) sheds light on the overall mortality trend. A recent study suggests that the most appropriate model for TFR is the generalized extreme value (GEV) distribution. This study proposes Exponentially Weighted Moving Average (EWMA) chart based on GEV distribution for monitoring TFRs and CDRs across different Middle East and North Africa (MENA) countries revealing a new finding that CDR also follows the GEV distribution. We introduce an innovative performance metric, Expected Absolute Loss EAL to assess the effectiveness of the control chart. Various quality metrics such as ARL, SDRL, MDRL, and EAL have been employed to assess the performance of the newly proposed GEV-EWMA control chart. The results indicate that the ARL bias stems from the GEV shape parameter which is affected by the nature of this asymmetric distribution. When symmetric limits are applied the bias persists however, using asymmetric limits significantly reduces the bias. These findings indicate that the GEV-EWMA chart outperforms, especially in detecting increasing extremeness signals.