A method for generating and testing reliable series of random numbers

Abstract

The concept of randomness is one of the most important ideas in the history of statistical analysis. Records of its application can be found in historical monuments since ancient times. In spite of its ancient history much confusion still surrounds its utility and real life applications. Nowadays, random numbers are being used in varity of applications such as statistics, cryptography, simulation, games and a mariad of applications. After the initial discussion of origins and problems of random number generation, this research introduces four of the most common generators used for producing random series: middle square, linear congruential, multiplicative congruential and finally Lagged Fibonacci algorithms. We use numerical examples to show how these methods generate random numbers. We also compare the strengths and weaknesses of each method. Moreover we suggest a new method for generating random numbers, we hope this method avoids the problems of previous methods. This study also introduces four tests commonly used to examine randomness: frequency test, runs test, poker test and autocorrelation test. We use these tests to analyse and compare the four methods of generating random methods. We also attempt to develop our own generator which through a ranking test was found to be more superior than the other four