Keywords

Asymptotic normality; Claim severity; Enriched Truncated Exponentiated distribution; Enriched Truncated Exponentiated Log-Logistic; Enriched Truncated Exponentiated Log-Normal; Kumaraswamy distribution; Loss models; L-statistics

Abstract

Statistical modeling of claim severity distributions is central to actuarial science and risk management, where parameter estimation must balance efficiency and robustness. Maximum likelihood estimation (MLE) is asymptotically efficient under correct model specification but sensitive to extreme observations and perturbations from the assumed distributional form. Robust L-estimators, including the method of trimmed moments (MTM) and the method of winsorized moments (MWM), provide alternatives based on linear combinations of order statistics, but their weighting structures either exclude or apply fixed modifications to extreme observations, restricting flexibility and potentially sacrificing efficiency.            This dissertation develops a smooth, data-adaptive weighting mechanism within the L-estimation framework for the recently introduced Enriched Truncated Exponentiated Generalized (ETE-G) family of distributions, with emphasis on the Log-Logistic (ETELL) and Log-Normal (ETELN) sub-models for heavy-tailed and moderate-tailed insurance losses. The proposed L-estimators use weight functions from probability density functions on (0, 1), with hyperparameters regulating the magnitude and location of down-weighting. This formulation generalizes classical trimmed and winsorized schemes by allowing continuous, data-range-wide adjustment of tail influence without removing observations or imposing fixed modifications. Two complementary strategies are developed: one based on varying transformation functions with common weights, and the other on varying weight functions with a common transformation. Observation-specific weights vary smoothly over the entire support, ensuring all observations contribute while limiting the influence of extreme order statistics.   Estimating equations are derived, and asymptotic theory established, including consistency, asymptotic normality, and variance expressions. Efficiency comparisons with MLE are provided under correct specification, together with robustness analysis under contamination. Monte Carlo simulations evaluate finite-sample performance, and an empirical study using Norwegian fire insurance data illustrates practical behavior. Results demonstrate that when MLE is affected by extreme observations, the proposed L-estimators remain stable with improved goodness-of-fit and predictive performance, supporting density-weighted L-estimation as a flexible approach for actuarial loss severity modeling.

Completion Date

2026

Semester

Spring

Committee Chair

Poudyal, Chudamani

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

School of Data, Mathematical, and Statistical Sciences

Format

PDF

Document Type

Dissertation

Identifier

DP0053115

Release Date

5-15-2027

Download

Available for download on Saturday, May 15, 2027

Share

COinS
 

Accessibility Statement

This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.