Pareto-S Distribution - Bleed, Salma Omar; Gnedela, Abd El-Salam M. (The 1st International Conference On Basic Sciences & Its Applictionss, 2024)
In this article, the Pareto distribution will be converted to a new distribution using the DUS method, with some statistical properties and estimation parameters of the new distribution being studied. It's named Pareto-S distribution. Some statistical properties of the Pareto-S distribution are obtained such as, median, mode, variance, moments, moment generating function, characteristic function, reliability, hazard function and Rényi entropy. Pareto-S Parameter Estimation by maximum likelihood method and Newton-Raphson procedure are addressed.  Finally, the estimation procedures to different simulated Pareto-S data sets each with pre-specified parameter values and varying sample sizes are applied, and the results of Newton-Raphson procedure compared with the results of the ML method, the results show that the ML seem to perform much better than the Newton-Raphson method for  the small sample sizes and the Newton-Raphson method seem to perform much better than  the ML for the large sample sizes.
Keywords: DUS Method; Reliability Function; Hazard Function; Maximum Likelihood Method; Newton-Raphson Procedure; Pareto Distribution; Rényi Entropy