Enhancing the Cosine-Lomax Distribution: A New Exponentiated Version with Improved Flexibility and Real-World Applications

In this paper, we introduce a novel flexible probability distribution called the Exponentiated Cosine Lomax distribution (ECLD), developed by compounding the exponentiated family with the cosine Lomax distribution. The proposed model incorporates an additional shape parameter, enhancing its flexibility to model complex real-world data with heavy tails, skewness, and non-monotonic hazard rates. We derive key statistical properties of the ECLD, including moments, moment-generating function, quantile function, and hazard rate. The model parameters are estimated using the maximum likelihood estimation (MLE) and maximum product of spacings (MPS) methods. A comprehensive simulation study is conducted to assess the consistency and efficiency of the estimators. To demonstrate the practical applicability of the ECLD, we analyze two real-world datasets. Comparative studies with existing models, including the Odd Frechet Lomax, half logistic Lomax, cosine Lomax, Lomax and sine Lomax distributions, reveal that the proposed ECLD provides a significantly better fit based on goodness-of-fit criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kolmogorov-Smirnov (K-S) test. The findings suggest that the ECL distribution is a robust alternative for modeling skewed and heavy-tailed data in various fields.