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Topic: Random number generation

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	Random Number Generation - Wolfram Mathematica
		Random number generation is at the heart of Monte Carlo estimates.
		Random number generation is also highly useful in estimating distributions for which closed-form results are not known or known to be computationally difficult.
		By default, RandomReal and RandomComplex generate machine-precision numbers.
	reference.wolfram.com /mathematica/tutorial/RandomNumberGeneration.html (3748 words)

	Random Number Generation :: Probability Distributions (Statistics Toolbox™)
		A binomial random number is the number of heads in N tosses of a coin with probability p of a heads on any single toss.
		If the goal is to generate a random number from a continuous distribution with pdf f, acceptance-rejection methods first generate a random number from a continuous distribution with pdf g satisfying f (x) ≤ cg (x) for some c and all x.
		Random numbers are generated from a distribution with a probability density function that is equal to or proportional to a proposal function.
	www.mathworks.com /access/helpdesk/help/toolbox/stats/bqttfc1.html (2486 words)

	Random Number Generation
		To satisfy the requirement that the computer is able to generate many "random" numbers quickly that come close to satisfying the desired theoretical properties, short algorithms which produce a sequence of pseudo-random numbers are often employed.
		Pseudo-random number generators should produce sequences of numbers which fall uniformly in the range from 0 to 1 and come close to passing various tests of independence.
		Pairs of independent random numbers should fall evenly in the unit square, and triples of independent random numbers should fall evenly in the unit cube.
	www.mathcs.duq.edu /larget/math496/random.html (803 words)

	RANDOM NUMBER GENERATION (LUC DEVROYE) (Site not responding. Last check: )
		We give random variate generators for the generalized hyperbolic secant distribution and related families such as Morris's skewed generalized hyperbolic secant family and a family introduced by Laha and Lukacs.
		To generate a random vector from a given ortho-unimodal density, several general-purpose algorithms are presented; and an experimental performance evaluation illustrates the potential efficiency increases that can be achieved by these algorithms versus naive rejection.
		The "Workshop on random number generators and highly uniform point sets", to be hel June 17-28, 2002, at the CRM in Montreal.
	cgm.cs.mcgill.ca /~luc/rng.html (1485 words)

	OMNeT++: Random number generation (Site not responding. Last check: )
		Generation is using the relationship to Bernoulli distribution (runtime is proportional to n).
		Returns a random integer from the negative binomial distribution with parameters n and p, that is, the number of failures occurring before n successes in independent trials with probability p of success.
		Generation is using the relationship to geometric distribution (runtime is proportional to n).
	www-personal.monash.edu.au /~swoon/omnetpp-doc/group__RandomNumbers.html (1346 words)

	Random Number Generation
		Theoretical properties are often hard to obtain (they require real math!), but one prefers a random number generator with a long period, low serial correlation, and a tendency not to "fall mainly on the planes." Statistical tests are performed with numerical simulations.
		Generally, a random number generator is used to estimate some quantity for which the theory of probability provides an exact answer.
		To use the random number generators, you do not need to know the details of what comprises the state, and besides that varies from algorithm to algorithm.
	rb-gsl.rubyforge.org /rng.html (768 words)

	Random number generation
		Random number generation by well researched algorithms should be able to provide extremely long series of numbers for which there is an infinitesimally small probability of finding a repeating pattern.
		This is not acceptable for many purposes, therefore, StatsDirect seeds the random number generator with a number taken from the computer's clock (the number of hundredths of a second which have elapsed since midnight).
		The random number generation section of the data menu enables you to specify seeds.
	www.statsdirect.com /help/randomization/rnd.htm (347 words)

	CSERD: Random Number Generation
		The "pseudo" in pseudo random refers to the fact that if you use a rule to generate a number, it is by definition not random, though it may appear so, and be close enough to random for all practical purposes.
		Most computational methods of generating a distribution of numbers that appears random use a process by which you apply a rule to one number to get another number, and then use that number to generate the next.
		That number replaces your seed, and is used as the seed for the next random number to be generated.
	www.shodor.org /refdesk/Resources/Algorithms/RandomNumbers (374 words)

	NIST.gov - Computer Security Division - Computer Security Resource Center
		NIST Special Publication (SP) 800-90, Recommendation for Random Number Generation Using Deterministic Random Bit Generators (Revised), specifies four DRBGs and briefly discusses entropy sources and methods for creating an RNG from an entropy source and an Approved DRBG.
		A workshop on random number generation was held from July 19-22, 2004 at NIST.
		Additional comments on the ANSI X9.82 and comments in general may be sent to ebarker@nist.gov or John.Kelsey@nist.gov.
	csrc.nist.gov /groups/ST/toolkit/random_number.html (331 words)

	The Laws of Cryptography: Pseudo-random Number Generation
		Random numbers are very widely used in simulations, in statistical experiments, in the Monte Carlo methods of numerical analysis, in other randomized algorithms, and especially in cryptography.
		This section focuses on random number generators used in simulation and numerical analysis, but for use in cryptography, the recommended random number generators are derived from cryptosystems, both conventional and public key.
		Knuth has other suggestions for efficient random number generators of high quality, where ``quality'' is measured by a variety of statistical tests that compare the output of the pseudo-random generator with true random numbers.
	www.cs.utsa.edu /~wagner/laws/rng.html (1190 words)

	Random Number Generation - Wolfram Demonstrations Project
		A random or pseudorandom number generator (RNG) is a computational or physical device designed to generate a random sequence of numbers.
		For binary sequences, the Demonstration also includes a sample segment of random bits that was produced by a hardware device whose randomness relies on a quantum physical process and another whose randomness relies on atmospheric noise.
		A normal sequence is a sequence whose digits show a uniform distribution, with all digits being equally likely; the 5-normality test partitions the whole sequence into substrings of length 1 to 5 and tests each for whether the standard variation of their frequency differs by an acceptable value (the statistical tolerance).
	demonstrations.wolfram.com /RandomNumberGeneration (462 words)

	Random Number Generation
		A fact learned in a standard first course in probability is that for any continuous random variable X with a cumulative distribution function F that has a unique inverse F^{-1}, F(X) is a uniform random variable on (0,1).
		For example, the binomial distribution with parameters n and p is the sum of n independent Bernoulli(p) random variables, the negative binomial distribution with parameters r and p is the sum of r independent geometric(p) random variables, and the gamma distribution with parameters alpha and lambda is a sum of alpha independent exponential(lambda) random variables.
		As long as the number of terms in the sum is not too large, these distributions may be efficiently simulated summing several generated pseudo-random numbers with the appropriate distribution.
	www.mathcs.duq.edu /larget/math496/random2.html (700 words)

	ComScire - The Random Number Generator Company. (Site not responding. Last check: )
		Coveyou, R. Random number generation is too important to be left to chance.
		Whittlesey, J. A comparison of the correlational behaviour of random number generators for the I.B.M. Canavos, G. A comparative analysis of two concepts in the generation of uniform pseudorandom numbers.
		Esmenjaud-Bonnardel, M. A procedure for the generation of pseudorandom numbers on the CAB 500.
	www.comscire.com /bibliography?SearchText=the&radHow=qryKeywords (2278 words)

	RANDOM NUMBER GENERATION (LUC DEVROYE)
		We give random variate generators for the generalized hyperbolic secant distribution and related families such as Morris's skewed generalized hyperbolic secant family and a family introduced by Laha and Lukacs.
		To generate a random vector from a given ortho-unimodal density, several general-purpose algorithms are presented; and an experimental performance evaluation illustrates the potential efficiency increases that can be achieved by these algorithms versus naive rejection.
		The "Workshop on random number generators and highly uniform point sets", to be hel June 17-28, 2002, at the CRM in Montreal.
	cg.scs.carleton.ca /~luc/rng.html (1485 words)

	Random Number Generation
		All generators are implicitly initialized to an unspecified state that does not vary from one program execution to another; they may also be explicitly initialized, or reinitialized, to a time-dependent state, to a previously saved state, or to a state uniquely denoted by an integer value.
		To enable the user to determine the suitability of the random number generators for the intended application, the implementation shall describe the algorithm used and shall give its period, if known exactly, or a lower bound on the period, if the exact period is unknown.
		If the generator period is sufficiently long in relation to the number of distinct initiator values, then each possible value of Initiator passed to Reset should initiate a sequence of random numbers that does not, in a practical sense, overlap the sequence initiated by any other value.
	www.adaic.org /standards/95lrm/html/RM-A-5-2.html (1360 words)

	Random Number Generation Utility Routines
		The utility routines for the random number generators allow the user to select the type of the generator (or to determine the type of the generator being used) and to set or retrieve the seed.
		− 1 or a GFSR generator or Mersenne Twister.
		In addition to controlling separate streams of random numbers, sometimes it is desirable to insure from the beginning that two streams do not overlap.
	www.vni.com /products/imsl/documentation/fort06/stat/NetHelp/randomnumbergenerationutilityroutines.htm (1708 words)

	Random number generation (Site not responding. Last check: )
		Seed to this LSHR based random number generator is generated with the help of a noise diode, an amplifier and a high-speed (10 megasamples per second) 12-bit analog-to-digital converter.
		A sample from the noise diode is used as the seed and is added periodically to the LSHR random number generator.
		Random numbers are needed at 50 ns intervals and these seeds are received at 100 ns intervals which means that every other random sample is from the noise diode and every other is synthetically produced in the shift register.
	www.uwasa.fi /cs/publications/2NWGA/node64.html (175 words)

	Xona.com - Minesweeper and Random Number Generation
		Ideally, this new number, generated via a complex algorithm within the function, is difficult to for a human to predict, even if she knows what the original input number was.
		In other words, show a person the first number (used as input into the function), and the second number (which the function outputs), and the distinction between the two should be complex enough that the person should not be able to discern any patterns.
		No matter how much randomness is used to generate the seed, even if you used a truly legitimate random source to generate it, there are still only 4.3 billion different ways to store the 32 bits of data that comprise the seed.
	xona.com /2004/07/27-2.html (1476 words)

	Cryptography:Random number generation - Wikibooks, collection of open-content textbooks
		The generation of random numbers is essential to cryptography.
		Any stochastic process (generation of random numbers) simulated by a computer, however, is not truly random, but pseudorandom; that is, the randomness of a computer is not from random radioactive decay of an unstable chemical isotope, but from predefined stochastic process.
		One common trait of random number generators is a domain mapped to all reals greater than or equal to 0 but less than or equal to 1.
	en.wikibooks.org /wiki/RandNum (440 words)

	Random Number Generation
		Unfortunately, generating random numbers is a task that looks a lot easier than it really is, primarily because it is fundamentally impossible to produce truly random numbers on any deterministic device.
		To evaluate a random number generator, several different tests should be used and the statistical significance of the results established.
		Generating random numbers according to a given nonuniform distribution can be a tricky business.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE142.HTM (1580 words)

	Random Number Generation (Site not responding. Last check: )
		The function srand() is used to seed or initialize the random number generator.
		It is also good to know that if you seed the random number generator with the same seed, it will produce the same set of random numbers each time.
		One way to obtain a random set of numbers is to use the time() function to seed the random number generator.
	www.programcpp.com /AppendixD/D_2.html (204 words)

	Random Number Generation
		The spectral test is known as a geometric quantity to assess lattices and, hence, to assign a figure of merit to certain (linear) random number generators.
		The quality of these generators (besides their speed and period length) is often measured via the equidistribution properties of their point sets, i.e, the set of vectors of successive values that they produce, from all possible seeds.
		We study a class of combined multiple recursive random number generators constructed in a way that each component runs fast and is easy to implement, while the combination enjoys excellent structural properties as measured by the spectral test.
	www.mcqmc.org /MCQMC2000/specialsessions/generation (604 words)

	Random Number Generation
		There are as many different random number generators as there are ways to search a string for a substring.
		These two random number generators take up very little space, have very long periods and other useful statistical properties, and are extremely fast — much, much faster than the standard random number generator that comes with your platform.
		The Mersenne Twister is a new random number generator, invented/discovered in 1996 by Matsumora and Nishimura.
	www.qbrundage.com /michaelb/pubs/essays/random_number_generation.html (933 words)

	20.1 Random Number Generation (Site not responding. Last check: )
		Multiple instances of the RNG class can be created to allow a simulation to draw random numbers from independent random number streams.
		For instance, a user who wants to generate the same traffic (based on some random process) in 2 different simulation experiments that compare different dropping algorithms that are themselves based on random processes may choose to base the traffic generation on one random number stream and the dropping algorithms on another stream.
		However, when using multiple RNG objects in a simulation care should be taken to insure that they are seeded in such a way as to guarantee that they produce independent, high-quality streams of random numbers.
	www.isi.edu /nsnam/ns/doc-stable/node205.html (157 words)

	CCS - FAQ: How can I generate a random number?
		To create a random number, we calculate the parity on a byte that has been ANDed with 0xb4.
		Another thought is to seed the random number generator with a counter from one of the timers.
		However, this example only uses 8 bit bytes for random number generation so you will have to edit it for a 16bit seed for full effect.
	www.ccsinfo.com /faq?33 (206 words)

	Integer Functions, Random Number, String Conversion, Searching and Sorting: <stdlib.h>
		Random numbers are useful in programs that need to simulate random events, such as games, simulations and experimentations.
		These are computed form a given formula (different generators use different formulae) and the number sequences they produce are repeatable.
		One common technique to introduce further randomness into a random number generator is to use the time of the day to set the seed, as this will always be changing.
	www.cs.cf.ac.uk /Dave/C/node16.html (908 words)

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