Method of Winsorized Moments for Robust Fitting of Truncated and Censored Lognormal Distributions

Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data

“…The analysis of grouped sample data has largely depended on maximum likelihood estimation (MLE). However, MLE can result in models that are overly sensitive to anomalies in the data distribution, such as contamination, Tukey (1960), or the presence of disproportionately heavy point masses at specific values, a scenario frequently encountered in the actuarial field, particularly within payment-per-payment and paymentper-loss data contexts, Poudyal et al (2023).…”

“…Studies by Brazauskas et al (2009); Zhao et al (2018) have, respectively, applied MTM and MWM to datasets with completely observed ground-up actuarial loss severity. In contexts of incomplete actuarial loss data, particularly for payment-per-payment and payment-per-loss, Poudyal (2021a) and Poudyal et al (2023) have, respectively, implemented MTM and MWM. These investigations have further established that trimming and winsorizing serve as effective strategies for enhancing the robustness of moment estimation in the presence of extreme claims, Gatti and Wüthrich (2023).…”

Model Uncertainty and Selection of Risk Models for Left-Truncated and Right-Censored Loss Data

“…In the actuarial literature, Brazauskas and Upretee (2019) studied various aspects of LTRC insurance loss data such as the probability density function (PDF), cumulative distribution function (CDF), and quantile function (QF), building up a framework to derive asymptotic distributions of parametric and empirical estimators. Moreover, Poudyal et al (2023) designed some robust parametric estimation procedures for the insurance payment data affected by deductibles, policy limits, and coinsurance factors. These authors clearly presented examples and showed how model uncertainty arises in the model fitting process of the actuarial loss data and how to deal with model mis-specification.…”