Speaker
Description
This paper presents an analysis of the impact of data clustering on the accuracy of Weibull distribution parameter estimation in strength tests of mineral fertilizer granules. Two approaches are compared: traditional clustering into fixed-width intervals and optimal clustering, derived from a correctly constructed Fisher information matrix for clustered data. Maximum likelihood estimators for data clustered according to optimal limits are also developed. The study was conducted on actual measurement data for three commercial fertilizers. Model fit was assessed using the chi-square test, and the Asymptotic Relative Efficiency (ARE) was calculated to compare the precision of scale and shape parameter estimation. The results showed that optimal clustering consistently increased the efficiency of shape parameter estimation and improved the p-values in the goodness-of-fit tests. It was also demonstrated that the choice of clustering method influences the assessment of distribution skewness and, consequently, the interpretation of phenomena related to granule failure mechanics. The obtained results confirm that in analyses based on grouped data, the use of optimal intervals allows for reducing information loss and improving the quality of statistical inference.
75002908166