Evaluating Burr XII Distribution as Crop Yield Probabilistic Model (CYPM‐BXII) Using Correction Function and Convex Optimization Approach

Abstract

This work examines the modeling of crop yield through a probabilistic approach and addresses the problems of efficiency and flexibility that have been compromised, particularly during operational decision‐making. Crop yield forecasting is inherently uncertain, requiring precise and manageable probabilistic models to enhance accuracy. A semiparametric approach using a generalized distribution called Burr XII (BXII) is considered here for crop yield probabilistic modeling (CYPM), emphasizing BXII's flexibility as a maximum likelihood estimator (MLE) and its potential to serve as the underlying distribution for a nonparametric estimator. This study aims to assess the efficacy of the BXII distribution as a semiparametric estimator (SPE) for crop yield, with a focus on enhancing both computational efficiency and modeling accuracy. This research employs a correction function and a convex optimization approach to investigate the proposed SPE. The SPE is designed based on a parametrically guided kernel density (PGKD) approach and is compared with the traditional kernel density (TKD/KDE) method. The BXII distribution is hypothesized to serve as a MLE underlying both the TKD and PGKD techniques for analyzing crop yield. A genetic algorithm (GA) is utilized to iteratively solve for the convexity parameter () and scaling constants ( α , β ). The analysis revealed that the value of the convexity parameter for the given crop yield data is approximately ≅ 0.99 across all scenarios, indicating that the MLE outperforms the TKD method. Performance analysis further demonstrated that both MLE and the PGKD approach are superior to TKD in terms of integrated sum square error (IISE). However, KDE remains competitive regarding Kullback–Leibler (KL) divergence and convergence rate, depending on data size. Overall, the results support the hypothesis that the BXII distribution is a promising candidate for a semiparametric model. This study builds on previous research by validating the applicability of the BXII distribution in agricultural production modeling. It underscores the potential of BXII to enhance crop yield forecasts in uncertain environments while addressing the trade‐off between computational efficiency and modeling quality that arises from the separate deployment of estimators. The findings indicate that BXII can serve as either a parametric or nonparametric estimator of agricultural yield, depending on the research objectives. Given the focus on operational choices related to crop output, it appears that choosing between the MLE and the SPE based on PGKD is of particular interest, with the latter offering a more balanced result.