قارن الطرق

	تخصيص احتياطيات الخسائر بطريقة السلم المتسلسل (نموذج ماك)	الاستدلال بالتمهيد	نموذج توزيع الخسائر
المجال	العلوم الاكتوارية	الإحصاء	العلوم الاكتوارية
العائلة	Regression model	Regression model	Regression model
سنة النشأة	1993	1979	2012
صاحب الطريقة	Thomas Mack	Bradley Efron	Klugman, Panjer & Willmot
النوع	Stochastic loss reserving model	Resampling-based inference	Parametric probability model
المصدر التأسيسي	Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.	Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. Annals of Statistics, 7(1), 1-26.	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
الأسماء البديلة	Development Factor Method, Link Ratio Method, Loss Development Method, Zincir Merdiven Yöntemi	bootstrap, bootstrap resampling, nonparametric bootstrap, Bootstrap Çıkarımı	Severity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı Modeli
ذات صلة	3	5	3
الملخص	Chain-Ladder Reserving is a stochastic actuarial method for estimating outstanding claim liabilities from a run-off triangle of cumulative paid losses. Formalized by Thomas Mack in 1993, it provides distribution-free estimates of reserve amounts along with their standard errors, making it a cornerstone of property-casualty insurance reserving and regulatory practice worldwide.	Bootstrap inference, introduced by Bradley Efron in 1979, estimates the sampling distribution of a statistic by repeatedly resampling the observed data with replacement. It requires no distributional assumption and produces reliable confidence intervals even in small samples.	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.