Research And Statistical Tests On Uniform Random Number Generators

Random number generators are used in many areas, with the improvement of the computational ability of the computer. For example: Monte-Carlo method on numerical analysis, statistical sampling technology, cryptography, and so on. Till now, there are a lot of generators such as the classical Fibonacci method, mid-square method, linear congruential method, feedback shift register method and combined method; the recent nonlinear congruential method, decimal fraction method, add-with-carry and substract-with-borrow methods, generalized feedback shift register method and MT method, and so on. Although a large amount of theoretical research has already been done on this subject, still there are some defects. In this paper, firstly it concerns with these precious random number generators simply, and then presents a new random number generator and several combined generators based on research work of the previous generators.In this paper, it also concerns with a large number of tests work on the random number sequences produced by these generators. For example, parameter tests, which involves with mean, 2-order matrix and variance; uniform tests, which includes chi-square test, K-S test and serial test; independence test, which concerns with correlation test, coloum-with-table test and run test and other type tests. All these tests are mainly developed with C language through the computer. Although different random number generators have different merits and defects, the tests results prove that the improved generators are not bad ones and have good statistical property, so they are of practical value.