Comparative Study of Estimation Methods for Kumaraswamy Weibull Regression Model: An Application to Economic Value-Added Data

Document Type : Original Article

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1 PhD Researcher

2 Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.

Abstract

This study investigates several parameter estimation techniques for the Kumaraswamy Weibull regression model using economic value-added data. Five methods are compared: maximum likelihood estimation (MLE), ordinary least squares (OLS), weighted least squares (WLS), Cramér-von Mises (CVM), and Anderson-Darling (AD). The analysis, based on quarterly data from five firms over 24 periods, shows that MLE consistently achieves the lowest values across the three information criteria (AIC, BIC, and HQIC). After identifying MLE as the optimal estimation technique, parameters for both Kumaraswamy Weibull and standard Weibull models were estimated. Statistical tests reveal the superiority of the Kumaraswamy Weibull model in handling economic value-added data, yielding a higher p-value (0.273) compared to the standard Weibull model (0.063). Additionally, the regression model based on the Kumaraswamy Weibull distribution demonstrates a superior fit (R² = 0.96 compared to 0.84) and aligns more closely with economic theory. In particular, economic value-added is found to be positively related to firm size and negatively related to both leverage and collection periods. The findings offer important methodological insights for selecting appropriate distributions and estimation methods in complex financial data modeling.

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