Several pseudorandom number generators are described and compared on the basis of cost of generation and length of period of the sequences that are produced. The major statistical tests, which are used to obtain a measure of randomness for the different generators are discussed and compared. Four pseudorandom number generators are programmed in GPSS and are used to generate interarrival and service times for an M/M/1 queuing system. The results of each of the trials are compared to the theoretical results which can be obtained from queuing theory.

Random numbers are a basic part in a Simulation Model, and they are also used in random sampling. These techniques are employed by quality engineers in the successful execution of their jobs. The every-day use of random numbers, however, often leads to a sense of complacency in he mind of engineers toward the exacting requirements that should be satisfied by the random number process to generate a genuine random number. Microcomputers have become a common and powerful tool that helps managers and engineers in their simulation experiments by providing sequences of random numbers. This research presents a sequence of eight tests to test the Radio Shack microcomputer system random number generator for uniformity and randomness; then, this Radio Shack random number generator is used to generate uniform and non-uniform deviates and a non-parametric test is performed to test these deviates for randomness. Two computer programs written in the BASIC language are used to test for randomness. The first one to test the Radio Shack random number generator and the second one to test the uniform and non-uniform deviates.

The continuous improvement in the speed of digital components in conjunction with reduction of size has brought about a revolutionary age of microprocessors. Mathematical functions, which at one time could only be implemented by complex analog circuitry, can now be easily implemented via microprocessors and high density digital components. Principles of random number generation must be understood in order to implement pseudo-random algorithms in a digital random frequency generator (DRFG) design. Chapter 1 is a discussion of several types of random number algorithms which have been used in the past and outlines the deficiencies and advantages associated with each individual algorithm. In particular, problems such a cycling and maximum period deficiency are discussed. The discussions in Chapter 1 lead to the selection of a random number algorithm which can be used in a DRFG design. There are other characteristics which should be observed in the evaluation of acceptable random number algorithms. In Chapter 2 three tests are described which can be applied in order to test the algorithm for the well-known uniformity and independence criteria. These tests are implemented in a Fortran program which is used to evaluated the algorithm selected in Chapter 1. The random number generator evaluation program (RNGEP) listing is presented in Appendix B. The results of the tests applied to the DRFG random number algorithm are presented in Appendix C.

This diploma thesis deals with creation of several random number generators. The data from these prototypes are then compared according to various aspects and statistical methods. The reader is familiar with the basic concepts, the existing random number generators and the technologies used.

The thesis deals with issues of random numbers, their generating and use in cryptography. Introduction of work is aimed to resolution of random number generators and pseudo--random number generators. There is also included often used dividing generators on software and hardware. We mention advantages and disadvantages of each type and area of their use. Then we describe examples of random and pseudorandom numbers, mainly hardware based on physical phenomenon such as the decay of radioactive material or use atmospheric noise. The following part is devoted to suggestion own random number generator and a description of its functionality. In the second half of the work we devote to the field of cryptography. We know basic types of cryptographic systems, namely symmetric and asymmetric cryptosystems. We introduce a typical representant the various type and their properties. At the end of the work we again return to our random number generator and verify the randomness generated numbers and obtained cryptograms.

International Telemetering Conference Proceedings / October 26-29, 1998 / Town & Country Resort Hotel and Convention Center, San Diego, California / In computer simulations of communication systems, linear congruential generators and shift registers are typically used to model noise and data sources. These generators are often assumed to be close to ideal (i.e. delta correlated), and an insignificant source of error in the simulation results. The samples generated by these algorithms have non-ideal autocorrelation functions, which may cause a non-uniform distribution in the data or noise signals. This error may cause the simulation bit-error-rate (BER) to be artificially high or low. In this paper, the problem is described through the use of confidence intervals. Tests are performed on several pseudo-random generators to access which ones are acceptable for computer simulation.

The "Ahrens method" is a very simple method for sampling from univariate distributions. It is based on rejection from piecewise constant hat functions. It can be applied analogously to the multivariate case where hat functions are used that are constant on rectangular domains. In this paper we investigate the case of distributions with so called orthounimodal densities. Technical implementation details as well as their practical limitations are discussed. The application to more general distributions is considered. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

Thesis (M.S.)--Florida State University, 2003. / Advisor: Michael Mascagni, Florida State University, College of Arts and Sciences, Dept. of Computer Science. Title and description from dissertation home page (viewed Mar. 2, 2004). Includes bibliographical references.

A rejection algorithm, called ``transformed density rejection", is presented. It uses a new method for constructing simple hat functions for a unimodal density $f$. It is based on the idea of transforming $f$ with a suitable transformation $T$ such that $T(f(x))$ is concave. The hat function is then constructed by taking the pointwise minimum of tangents which are transformed back to the original scale. The resulting algorithm works very well for a large class of distributions and is fast. The method is also extended to the two- and multidimensional case. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Generating random variates as generalisation of a given sample is an important task for stochastic simulations. The three main methods suggested in the literature are: fitting a standard distribution, constructing an empirical distribution that approximates the cumulative distribution function and generating variates from the kernel density estimate of the data. The last method is practically unknown in the simulation literature although it is as simple as the other two methods. The comparison of the theoretical performance of the methods and the results of three small simulation studies show that a variance corrected version of kernel density estimation performs best and should be used for generating variates directly from a sample. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing