article · Modern Journal of Statistics
A new three-parameter probability model, known as the power Mira distribution, has been developed to capture diverse statistical patterns in heavy-tailed data. By incorporating an additional shaping parameter, the model flexibly handles unimodal distributions, declining trends, and both left and right skewness. These properties make it particularly useful for modelling risk in actuarial science and insurance analytics. Theoretical analysis establishes the fundamental statistical properties of the distribution and provides a framework for parameter estimation. Numerical simulations confirm the accuracy and efficiency of estimators for key risk metrics, including value-at-risk and tail value-at-risk. When tested on real-world insurance loss data, the distribution demonstrated superior goodness-of-fit and flexibility compared to established models, confirming its utility for financial modelling and risk assessment.
Accurately calculating potential losses is essential for insurers and financial institutions managing catastrophic risks. Traditional statistical tools often struggle with heavy-tailed and skewed data. By providing better mathematical flexibility and reliable estimates of extreme loss metrics, this model enables risk professionals to forecast extreme events more accurately and make sounder financial provisions.
The distribution is directly applicable to actuarial science, financial modelling, and insurance risk assessment. Actuaries, risk managers, and financial analysts can integrate the parameter estimation framework and risk metrics into loss-modelling software. Having been tested and validated against real-world insurance loss datasets, the model is at an applied and tested stage, ready for adoption in quantitative risk and underwriting workflows.
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This study presents the power Mira distribution, an innovative three-parameter probability model that improves baseline distributions by including an extra shaping parameter. The suggested distribution has exceptional adaptability in representing various data characteristics, such as left and right skewness, declining trends, and unimodal patterns. These characteristics render it exceptionally appropriate for modeling risk-related data, an essential component of actuarial science and insurance analytics. We do an extensive theoretical study, delineating essential statistical features and offering a robust framework for parameter estimation. Critical risk metrics, including value-at-risk and tail value-at-risk, are calculated and assessed using comprehensive numerical simulations, validating the precision and efficacy of the suggested estimators. We illustrate the practical value of the power Mira distribution by applying it to a real-world insurance loss dataset and comparing its performance with established models. The findings underscore its exceptional goodness-of-fit and flexibility, affirming its capability as an effective instrument for risk assessment and financial modeling.
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DOI: 10.64389/mjs.2025.01108
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