The serial test for linear congruential pseudo-random numbers
نویسندگان
چکیده
منابع مشابه
The Serial Test for Linear Congruential Pseudo-random Numbers
Let m>2 and r be integers, let y0 be an integer in the least residue system mod m, and let X be an integer coprime to m with X ^ ± 1 (mod m) and (X ~ l)y0 + r ^ 0 (mod m). A sequence y0,yl9...of integers in the least residue system mod m is generated by the recursion yn+ x = Xyn + r (mod m) for n = 0, 1, . . . . In the homogeneous case r = 0 (mod m), one chooses y0 to be coprime to m. The seque...
متن کاملThe Serial Test for Congruential Pseudorandom Numbers Generated by Inversions
Two types of congruential pseudorandom number generators based on inversions were introduced recently. We analyze the statistical independence properties of these pseudorandom numbers by means of the serial test. The results show that these pseudorandom numbers perform satisfactorily under the serial test. The methods of proof rely heavily on bounds for character sums such as the Weil-Stepanov ...
متن کاملOn the Distribution of Pseudo-Random Numbers Generated by the Linear Congruential Method. Ill
The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method, both homogeneous and inhomogeneous, is estimated for parts of the period that are somewhat larger than the square root of the modulus. The analogous problem for an arbitrary linear congruential generator modulo a prime is also considered, the result being particularly interesting for maximal peri...
متن کاملOn the Distribution of Pseudo -Random Numbers Generated by the Linear Congruential Method. II
The discrepancy of a sequence of pseudo-random numbers generated by the linear congruential method is estimated for parts of the period which are somewhat larger than the square root of the modulus. Applications to numerical integration are mentioned.
متن کاملOn the Distribution of Pseudo-Random Numbers Generated by the Linear Congruential Method
The discrepancy of sequences of pseudo-random numbers generated by the linear congruential method is estimated, thereby improving a result of Jagerman. Applications to numerical integration are mentioned. Let m be a modulus with primitive root X, and let y0 be an integer in the least residue system modulo m with g.c.d.(y0, m) = 1. We generate a sequence y0, yu of integers in the least residue s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1978
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1978-14472-3