A MODIFIED TRANSMUTED SINE DAGUM DISTRIBUTION: PROPERTIES, ESTIMATION, AND APPLICATIONS - Abdullahi, Ibrahim; Dalah, Musa Chiwa (FUDMA Journal of Sciences, 2026)
A new flexible distribution, termed the Power Sine Sine Dagum (PSSD) distribution, is introduced by applying a power sine transformation to the classical Dagum model. The proposed construction incorporates an additional shape parameter, thereby enhancing the ability of the baseline distribution to capture complex tail behavior and varying degrees of skewness. Several structural properties of the model are derived, including explicit expressions for the probability density function, cumulative distribution function, survival and hazard functions, quantile function, and moments. Parameter estimation is developed within both maximum likelihood and Bayesian frameworks. A Monte Carlo simulation study is conducted to evaluate finite-sample performance, with results indicating that the maximum likelihood estimator may exhibit instability in small samples, whereas the Bayesian estimator provides more stable and accurate inference. The practical performance of the model is illustrated using real datasets. The results show that the PSSD model achieves higher log-likelihood values and lower AIC, together with smaller goodness-of-fit statistics (KS, AD, and CvM), compared to the classical Dagum distribution. These findings demonstrate that the proposed model provides a flexible and effective tool for modeling heavy-tailed data
Keywords: Dagum distribution; Sine transformation; Heavy-tailed distribution; Maximum likelihood; Bayesian