A Hybrid Cosine Inverse Lomax-G Family of Distributions with Applications in Medical and Engineering Data

Abstract

: Statistical distributions are essential for modelling real-world phenomena in fields such as medicine, environmental science, and engineering. However, classical distributions often fail to capture complex data features like skewness and heavy tails. This study introduces a novel hybrid family of distributions, the cosine inverse Lomax (CIL)-G family, by merging the cosine-G and inverse Lomax-G families. The proposed family demonstrates enhanced flexibility and includes sub models applicable across diverse fields. Key statistical properties, including moments, entropy measures, and the quantile function, are derived. Parameter estimation is conducted using maximum likelihood, least squares, and weighted least squares techniques. Monte Carlo simulations are employed to examine the behaviour of the estimators for a specific model, the CIL-exponentiated Weibull (CILEW). The simulation results indicate that as the sample size increases, the bias and root mean squared error of the estimators decrease, demonstrating the consistency of the estimation techniques. The CILEW model is applied to three real-world datasets: (1) 40 turbocharger failure times from engineering, (2) 20 pain relief durations from medical data, and (3) 35 growth hormone treatment times from medical data. Performance is assessed using goodness-of-fit metrics such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), and Kolmogorov-Smirnov (KS) tests. The CILEW model outperforms competing models, by achieving the lowest AIC values of 171.62, 41.096, 165.44 and BIC values of 180.07, 46.074, 173.22 across the three datasets, along with the highest KS p-values of 0.8786, 0.9680, 0.9640, respectively. The proposed family provides a versatile framework for modelling complex datasets, making it a valuable tool for reliability engineering, healthcare analytics, and predictive modelling applications.