On the Sine Inverse Lomax Burr III Distribution with Application to Monthly Actual Tax Revenue Data

Advances in probability distributions are important for modelling complex data across fields such as actuarial science, environmental science, biomedical science, economics, finance, and insurance. Classical distributions often have limitations when dealing with highly skewed data, heavy tails, or unusual failure patterns. To address these challenges, this study introduces the Sine Inverse Lomax Burr III distribution, a new flexible model that combines the tail behaviour of the Burr III distribution with the skewness-control properties of the sine inverse transformation. Statistical properties, including quantiles, moments, moment generating functions, and order statistics, are derived. Some risk measures, including the value at risk, tail value at risk, and tail variance, are derived and studied. Parameter estimation is performed using five different estimation techniques: maximum likelihood estimation, least squares, weighted least squares, percentile matching, and Anderson–Darling. The usefulness of the proposed model is demonstrated using monthly tax revenue data. The results show that the SILBIII distribution performs better than the competing distributions. The proposed model is an alternative model suitable for modeling data in finance, actuarial, and related fields.