10 0, we Vue Tequired. It may number and is called Fo18 The congruence random number generator may be of the additive, multiplicative or mixed type Equation (13. 1) gives the mixed type If a = 1, the expression (13.1) reduces to the additive type as in expression (13.2). 1.1; + b) (modulo m). (132) If b = 0, the congruence method is called the multiplicative type, as in equation (13.3). "" ar, (modulo m). (13.3) The multiplicative methods are considered better than the additive methods and as good as the mixed methods. The generation of random numbers by these congruence methods is demonstrated in example 13.8-1. The selection of the values for the constants a, b and m is very important, because on them depends the length of the sequence of random numbers, after which the sequence repeats. It is not possible to generate a non-repeating sequence of numbers with these methods. However, a sufficiently long string of random numbers can be obtained by making a suitable selection of constants. Since the number can be predicted from r, and the whole string of random numbers is reproducible, the numbers obtained are not truly random. They are called pseudo-random numbers, and the method is termed as the pseudo-random number generator The validation of a pseudo-random number generator is very essential, before putting it to use. A number of tests have been proposed in the literature for testing the randomness of a sequence. A sequence of random numbers is considered to be adequately random, if its uniformity is assured, and the successive numbers in the sequence are independent The chi-square test of goodness of fit is employed to check that the sequence of numbers is generated from a (0, 1) uniform distribution. The randomness or independence test is used to check that the successive numbers are not correlated. One of the most effective methods for this purpose is the poker test. b 58 Most of the computer systems have a subroutine available for generating - - numbers. In DEC-20 computer system, a random number (say Y) is generated by using the following statement Y-RAN (x). where x may be any number of alphabet. EXAMPLE 13.8-1 The procedure of random number generation can be illustrated by taking some values for the constants a, b and m in equations (13.1) to (13.3). Let a = 16,6 - 18 and m - 23. (a) Mixed Congruence Method +1 = (ar, + b) (modulo m). Taking 16x1 +18 34 = 1 + remainder 11, 23 23 16x 11+18_194 12 = 8 + remainder 10. 23 23 -1