The article explores order statistics for different types of random variables, focusing on calculating moments for distributions like Beta, Erlang, and Frechet. The researchers introduced a new method using moment generating functions for Exponential and Erlang distributions. They also looked at L-moments and Trimmed L-moments for various distributions. Additionally, they used approximations for outliers following normal or gamma distributions. The study included order statistics and moments for the Sine square distribution. Finally, they examined moments for discrete random variables like Geometric, Binomial, and Poisson.