Expressing the randomity of events – An analysis of random number generation with given distributions

In cases where it is necessary to generate random numbers that obey specific distributions, some of those distributions can be expressed as mathematical functions while others cannot. This is especially the case for epidemiological, medical, and pharmaceutical investigations, where more accurate methods, utilising actual distribution (from survey and experimental data) to generate random numbers may be required. In this study, three methods are analyzed to demonstrate simple computation examples. These methods include: inverse transform,acceptance-rejection, and Monte-Carlo simulations. Their applications are explored from a data analysis point of view. Additionally, this article discusses a flexible and practical approach of statistical measures optimization, which approximates the solution by fitting the statistical measures.