Generate soft random numbers with a multi-focus approach

Random number generation is one of the most fundamental topics in statistics and data science. Random numbers are widely used in many fields such as statistical simulations, machine learning, education, defense industry, computer games. In this study, an algorithm for generating soft random numbers with variable discrepancy is developed using random number generators. The formulation of the proposed soft random numbers and the formulations of their moments are calculated. A soft random number generator, which is an approach to bridge the quasi-random numbers used in many applications and the pseudo-random numbers, has been developed. The softening parameter used in the development of soft random numbers can take a value between [0,1]. If the softening parameter is 0, grid quasi-random numbers are generated, if it is close to zero, quasi-random numbers, and if it is 1, pseudo-random numbers are generated. It has been observed in the simulations that the size of the discrepancy increases regularly as the softening parameter of the soft random numbers generated in different sample sizes from five different distributions increases. All soft random numbers generated in the simulations were tested for three different goodness of fit. It was observed that as the soft parameter decreased, the percentage of rejection of the hypothesis decreased and the type I error of the hypothesis decreases.