A Million Random Digits with 100,000 Normal Deviates

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Lines 10580-10594, columns 21-40, from A Million Random Digits with 100,000 Normal Deviates Random digits.png
Lines 10580–10594, columns 21–40, from A Million Random Digits with 100,000 Normal Deviates

A Million Random Digits with 100,000 Normal Deviates is a random number book by the RAND Corporation, originally published in 1955. The book, consisting primarily of a random number table, was an important 20th century work in the field of statistics and random numbers.

Contents

Production and background

It was produced starting in 1947 by an electronic simulation of a roulette wheel attached to a computer, the results of which were then carefully filtered and tested before being used to generate the table. The RAND table was an important breakthrough in delivering random numbers, because such a large and carefully prepared table had never before been available. In addition to being available in book form, one could also order the digits on a series of punched cards.

The table is formatted as 400 pages, each containing 50 lines of 50 digits. Columns and lines are grouped in fives, and the lines are numbered 00000 through 19999. The standard normal deviates are another 200 pages (10 per line, lines 0000 through 9999), with each deviate given to three decimal places. There are 28 additional pages of front matter.

Utility

The main use of the tables was in statistics and the experimental design of scientific experiments, especially those that used the Monte Carlo method; in cryptography, they have also been used as nothing up my sleeve numbers, for example in the design of the Khafre cipher. The book was one of the last of a series of random number tables produced from the mid-1920s to the 1950s, after which the development of high-speed computers allowed faster operation through the generation of pseudorandom numbers rather than reading them from tables.

2001 edition

The book was reissued in 2001 ( ISBN   0-8330-3047-7) with a new foreword by RAND Executive Vice President Michael D. Rich. It has generated many humorous user reviews on Amazon.com. [1]

Sample

The digits (sequence A002205 in the OEIS ) begin:

10097 32533  76520 13586  34673 54876  80959 09117  39292 74945

Related Research Articles

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A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's seed. Although sequences that are closer to truly random can be generated using hardware random number generators, pseudorandom number generators are important in practice for their speed in number generation and their reproducibility.

Linear congruential generator

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Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

Hardware random number generator Cryptographic device

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Mathematical table List of values of a mathematical function

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Stochastic refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a stochastic process is also referred to as a random process.

Maurice Kendall British statistician

Sir Maurice George Kendall, FBA was a prominent British statistician. The Kendall tau rank correlation is named after him.

Middle-square method

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Monte Carlo integration Numerical technique

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. It is a particular Monte Carlo method that numerically computes a definite integral. While other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand is evaluated. This method is particularly useful for higher-dimensional integrals.

A random password generator is software program or hardware device that takes input from a random or pseudo-random number generator and automatically generates a password. Random passwords can be generated manually, using simple sources of randomness such as dice or coins, or they can be generated using a computer.

Random number tables have been used in statistics for tasks such as selected random samples. This was much more effective than manually selecting the random samples. Nowadays, tables of random numbers have been replaced by computational random number generators.

Random number generation Producing a sequence that cannot be predicted better than by random chance

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The Marsaglia polar method is a pseudo-random number sampling method for generating a pair of independent standard normal random variables. While it is superior to the Box–Muller transform, the Ziggurat algorithm is even more efficient.

Computational statistics Interface between statistics and computer science

Computational statistics, or statistical computing, is the bond between statistics and computer science. It means statistical methods that are enabled by using computational methods. It is the area of computational science specific to the mathematical science of statistics. This area is also developing rapidly, leading to calls that a broader concept of computing should be taught as part of general statistical education.

Randomness Apparent lack of pattern or predictability in events

In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.

A standard normal deviate is a normally distributed deviate. It is a realization of a standard normal random variable, defined as a random variable with expected value 0 and variance 1. Where collections of such random variables are used, there is often an associated assumption that members of such collections are statistically independent.

Pseudo-random number sampling or non-uniform pseudo-random variate generation is the numerical practice of generating pseudo-random numbers that are distributed according to a given probability distribution.

Random number book

A random number book is a book whose main content is a large number of random numbers or random digits. Such books were used in early cryptography and experimental design, and were published by the Rand Corporation and others. The Rand corporation book A Million Random Digits with 100,000 Normal Deviates was first published in 1955 and was reissued in 2001. A sequel, A Million And One Random Digits was published in 2022.

References

  1. Heffernan, Virginia (January 15, 2010). "The Reviewing Stand". The New York Times Magazine . Retrieved 2011-03-09.

Additional sources