Reaoboka-Enoch-Thamae/Motor-Insurance-Analysis

Motor insurance portfolio analysis using PCA, Chi-Square testing and Poisson modelling in R | STAT1011Y | University of Mauritius # Motor Insurance Portfolio Analysis **STAT1011Y – Statistical Methods | University of Mauritius | 2025/2026** A group statistical analysis of a 1,200-policy motor insurance portfolio and daily claim count data, completed as part of the BSc Actuarial Studies programme. All analysis was done in R. --- ## Project Overview | Problem | Topic | Method | |---|---|---| | 1 | Risk Profiling & Dimension Reduction | Principal Component Analysis (PCA) | | 2 | Association Between Categorical Variables | Pearson's Chi-Square Test of Independence | | 3 | Claim Frequency Analysis | Poisson Goodness-of-Fit Test | --- ## Problem 1 – Risk Profiling (PCA) Explored the underlying risk structure of the motor insurance portfolio using PCA on 8 variables (age, vehicle age, premium, no-claims discount, past claims count, past total paid, annual mileage, engine power). **Key findings:** - 3 principal components retained, explaining ~55% of total variance - PC1 captures claims history vs. no-claims discount (high-risk vs. low-risk policyholders) - PC2 captures vehicle power and usage patterns - PC3 captures driver and vehicle age effects - Robustness confirmed by repeating PCA without premium — component structure remained stable - Distinct risk profiles identified: Young Power Drivers, High-Mileage Commercial Users, Aged Risk, Low Discount High Claim --- ## Problem 2 – Chi-Square Test of Independence Investigated whether claim type (Bodily Injury, Other, Property, Windscreen) and transmission type (Automatic, Manual) are independent. **Key findings:** - χ² = 8.0551, df = 3, p-value = 0.0449 - Rejected H₀ at the 5% level — evidence of association between claim type and transmission type - Standardised residuals showed Windscreen claims on Automatic vehicles (residual = 2.45) as the primary driver of the association --- ## Problem 3 – Poisson Claim Frequency Analysis Assessed whether daily claim counts from 365 days of portfolio data follow a Poisson distribution. **Key findin …