A New Logistic Distribution and Its Properties, Applications and PORT-VaR Analysis for Extreme Financial Claims

Abstract

This paper introduces a new extension of exponentiated standard logistic distribution. Some important statistical properties of the novel family of distributions are discussed. A simulation study is also conducted to observe the behavior of the estimated parameter using several estimation methods. The adaptability as well as the flexibility of the new model is checked through two real-life applications. A comprehensive financial risk assessment is conducted using multiple actuarial risk measures: Peaks Over Random Threshold Value-at-Risk, Value-at-Risk, Tail Value-at-Risk, the risk-adjusted return on capital and the Mean of Order P. These indicators offer a nuanced view of risk by capturing different aspects of tail behavior, which are critical in understanding potential extreme losses. These risk indicators are applied to analyze actuarial financial claims data, providing a robust framework for assessing financial stability and decision-making in the face of uncertainty. © 2025 by the authors.