PowerPoint Presentation

RANDOM NUMBER. UNIT 5.

Random Number Random numbers are samples drawn from a uniformly distributed random variable between some satisfied intervals, they have equal probability of occurrence. Random numbers are a necessary basic ingredient (element) in the simulation of almost all discrete systems. Most computer languages have a subroutine, object, or function that will generate a random number..

Properties of Random Numbers Uniformity , i.e. they are equally probable every where Independence , i.e. the current value of a random variable has no relation with the previous values.

Types of random numbers There are three types of random numbers, quasi- , pseudo- and true- random numbers. 1.True Random Number: True random numbers are gained from physical processes like radioactive decay or also rolling a dice. But rolling a dice is difficult, perhaps someone could control the dice so well to determine the outcome ..

2.Pseudo Random Number: These numbers are generated by a computer or that is to say, by an algorithm and because of this not truly random. Every new number is generated from the previous ones by an algorithm..

3. Quasi Random Number : Quasi (Virtual) random numbers are not designed to appear random, rather to be uniformly distributed. One aim of such numbers is to reduce and control errors in Monte Carlo simulations..

Testing for Randomness The tests can be placed in two categories according to the properties of interest. Testing for uniformity Testing for independence..

Testing for uniformity The testing for uniformity can be achieved through different frequency test. These tests use the Kolmogorov-Smirnov or the chi- square test to compare the distribution of the set of numbers generated to a uniform distribution. Hence in this category we will discuss two types of test.

1.The Kolmogorov-Smirnov (KS) test. This test compares the continuous cdf , F(x), of the uniform distribution to the empirical cdf , S N (x), of the sample of N observations. By definition, F(x) = x, 0 <= x <= 1 If the sample from the random-number generator is R 1 ,R 2 ,… R N , then the empirical cdf , S N (X), is defined by.

The Chi-square Test • The chi-square test uses the sample statistic.