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| Verallgemeinerte Kleinste Quadrate (GLS)× | Verlustverteilungsmodell× | |
|---|---|---|
| Fachgebiet≠ | Statistik | Versicherungsmathematik |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1935 | 2012 |
| Urheber≠ | Alexander Craig Aitken | Klugman, Panjer & Willmot |
| Typ≠ | Linear estimator | Parametric probability model |
| Wegweisende Quelle≠ | Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48. DOI ↗ | Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2012). Loss Models: From Data to Decisions (4th ed.). Wiley. ISBN: 978-1-118-31532-3 |
| Aliasnamen≠ | GLS, Aitken estimator, EGLS, feasible GLS | Severity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı Modeli |
| Verwandt | 3 | 3 |
| Zusammenfassung≠ | Generalized Least Squares (GLS) is a linear regression estimator that extends ordinary least squares to handle situations where the error terms are correlated or have non-constant variance (heteroscedasticity). Introduced by Alexander Craig Aitken in 1935, GLS achieves the Best Linear Unbiased Estimator (BLUE) under a general error covariance structure by weighting observations according to their precision, providing a theoretical bridge between OLS and modern linear mixed models. | A Loss Distribution Model is a parametric statistical framework used in actuarial science to characterise the probabilistic behaviour of insurance claim amounts and frequencies. Developed comprehensively by Klugman, Panjer, and Willmot in their foundational text Loss Models: From Data to Decisions (first edition 1998, fourth edition 2012), these models underpin premium rating, reserving, reinsurance pricing, and regulatory capital calculations across the insurance and risk-management industries. |
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