DERIVATION OF THE SINE EXPONENTIATED LOMAX DISTRIBUTION FOR MODELLING RIGHT SKEWED AND HEAVY TAILED DATA

Abstract

This study introduces the Sine-Exponentiated Lomax distribution, a three-parameter model designed for modeling heavy-tailed and right-skewed data. The probability density function, cumulative distribution function, and key mathematical properties including moments, quantile function, and entropy measures were derived. Parameters were estimated using maximum likelihood estimation, with simulation studies confirming estimator consistency and asymptotic normality across sample sizes from 50 to 2000 observations. The model's practical utility was demonstrated through four real-world applications: S&P 500 returns (finance), earthquake damage magnitudes (seismology), cancer remission times (biostatistics), and geyser eruption intervals (environmental science). In all cases, the S-EL distribution outperformed established models including the exponentiated Lomax, Weibull, and Burr distributions based on AIC, BIC, and other goodness-of-fit criteria. The distribution provides researchers with a robust, flexible tool for extreme-value modeling while maintaining mathematical coherence and computational practicality.