The prediction of missing order statistics for the Generalized Extreme Value distribution is investigated, with a focus on the Fréchet, Gumbel, and Weibull subtypes governed by the shape parameter γ. This paper first establishes a necessary and sufficient condition for the existence of conditional moments of order statistics based on the domain of γ. We then derive predictors using three distinct methods: the best unbiased predictor, the conditional median predictor, and the conditional average predictor. A comprehensive simulation study reveals that the optimal method is distribution-dependent. For the Gumbel distribution, the best unbiased predictor provides superior accuracy and robustness. For the Fréchet distribution, the best unbiased predictor is unequivocally superior, while the conditional average predictor and the conditional median predictor demonstrate significant bias and instability. For the Weibull distribution, the choice is critically sensitive to γ, best unbiased predictor is preferred for milder shapes, whereas the conditional average predictor is more robust for stronger shapes. These findings provide a clear, evidence-based framework for selecting the appropriate prediction method in extreme value analysis. To demonstrate the performance of the proposed methods, a numerical example utilizing a real-world data set is provided.
Almasi, I. and Esmailzadeh, N. (2025). Prediction of missing order statistics for generalized extreme value distribution. Journal of Statistical Modelling: Theory and Applications, 6(2), 25-44. doi: 10.22034/jsmta.2026.23689.1195
MLA
Almasi, I. , and Esmailzadeh, N. . "Prediction of missing order statistics for generalized extreme value distribution", Journal of Statistical Modelling: Theory and Applications, 6, 2, 2025, 25-44. doi: 10.22034/jsmta.2026.23689.1195
HARVARD
Almasi, I., Esmailzadeh, N. (2025). 'Prediction of missing order statistics for generalized extreme value distribution', Journal of Statistical Modelling: Theory and Applications, 6(2), pp. 25-44. doi: 10.22034/jsmta.2026.23689.1195
CHICAGO
I. Almasi and N. Esmailzadeh, "Prediction of missing order statistics for generalized extreme value distribution," Journal of Statistical Modelling: Theory and Applications, 6 2 (2025): 25-44, doi: 10.22034/jsmta.2026.23689.1195
VANCOUVER
Almasi, I., Esmailzadeh, N. Prediction of missing order statistics for generalized extreme value distribution. Journal of Statistical Modelling: Theory and Applications, 2025; 6(2): 25-44. doi: 10.22034/jsmta.2026.23689.1195
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