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George Marsaglia
George Marsaglia (March 12, 1924 – February 15, 2011) was an American mathematician and computer scientist. He is best known for creating the diehard tests, a suite of software for measuring statistical randomness. Research on random numbers George Marsaglia established the lattice structure of linear congruential generators in the paper "Random numbers fall mainly in the planes", later termed the Marsaglia's theorem. This phenomenon means that ''n''-tuples with coordinates obtained from consecutive use of the generator will lie on a small number of equally spaced hyperplanes in ''n''-dimensional space. He also developed the diehard tests, a series of tests to determine whether or not a sequence of numbers have the statistical properties that could be expected from a random sequence. In 1995 he published a CD-ROM of random numbers, which included the diehard tests. His diehard paper came with the quotation "Nothing is random, only uncertain" attributed to ''Gail Gasram'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denver, Colorado
Denver () is a consolidated city and county, the capital, and most populous city of the U.S. state of Colorado. Its population was 715,522 at the 2020 census, a 19.22% increase since 2010. It is the 19th-most populous city in the United States and the fifth most populous state capital. It is the principal city of the Denver–Aurora–Lakewood, CO Metropolitan Statistical Area and the first city of the Front Range Urban Corridor. Denver is located in the Western United States, in the South Platte River Valley on the western edge of the High Plains just east of the Front Range of the Rocky Mountains. Its downtown district is immediately east of the confluence of Cherry Creek and the South Platte River, approximately east of the foothills of the Rocky Mountains. It is named after James W. Denver, a governor of the Kansas Territory. It is nicknamed the ''Mile High City'' because its official elevation is exactly one mile () above sea level. The 105th meridian we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiply-with-carry
In computer science, multiply-with-carry (MWC) is a method invented by George Marsaglia for generating sequences of random integers based on an initial set from two to many thousands of randomly chosen seed values. The main advantages of the MWC method are that it invokes simple computer integer arithmetic and leads to very fast generation of sequences of random numbers with immense periods, ranging from around 2^ to 2^. As with all pseudorandom number generators, the resulting sequences are functions of the supplied seed values. General theory An MWC generator is a special form of Lehmer random number generator x_n = bx_ \bmod p which allows efficient implementation of a prime modulus p much larger than the machine word size. Normal Lehmer generator implementations choose a modulus close to the machine word size. An MWC generator instead maintains its state in base b, so multiplying by b is done implicitly by shifting one word. The base b is typically chosen to equal the compute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Xorshift
Xorshift random number generators, also called shift-register generators, are a class of pseudorandom number generators that were invented by George Marsaglia. They are a subset of linear-feedback shift registers (LFSRs) which allow a particularly efficient implementation in software without the excessive use of sparse polynomials. They generate the next number in their sequence by repeatedly taking the exclusive or of a number with a bit-shifted version of itself. This makes execution extremely efficient on modern computer architectures, but it does not benefit efficiency in a hardware implementation. Like all LFSRs, the parameters have to be chosen very carefully in order to achieve a long period. For execution in software, xorshift generators are among the fastest non- cryptographically-secure random number generators, requiring very small code and state. However, they do not pass every statistical test without further refinement. This weakness is amended by combining them with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subtract With Carry
Subtract-with-carry is a pseudorandom number generator: one of many algorithms designed to produce a long series of random-looking numbers based on a small amount of starting data. It is of the lagged Fibonacci type introduced by George Marsaglia and Arif Zaman in 1991.A New Class of Random Number Generators George Marsaglia and Arif Zaman, The Annals of Applied Probability, Vol. 1, No. 3, 1991 "Lagged Fibonacci" refers to the fact that each random number is a function of two of the preceding numbers at some specified, fixed offsets, or "lags". Algorithm Sequence generated by the subtract-with-carry engine may be described by the |
Multiply-with-carry
In computer science, multiply-with-carry (MWC) is a method invented by George Marsaglia for generating sequences of random integers based on an initial set from two to many thousands of randomly chosen seed values. The main advantages of the MWC method are that it invokes simple computer integer arithmetic and leads to very fast generation of sequences of random numbers with immense periods, ranging from around 2^ to 2^. As with all pseudorandom number generators, the resulting sequences are functions of the supplied seed values. General theory An MWC generator is a special form of Lehmer random number generator x_n = bx_ \bmod p which allows efficient implementation of a prime modulus p much larger than the machine word size. Normal Lehmer generator implementations choose a modulus close to the machine word size. An MWC generator instead maintains its state in base b, so multiplying by b is done implicitly by shifting one word. The base b is typically chosen to equal the compute ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marsaglia Polar Method
The Marsaglia polar method is a pseudo-random number sampling method for generating a pair of independent standard normal random variables. Standard normal random variables are frequently used in computer science, computational statistics, and in particular, in applications of the Monte Carlo method. The polar method works by choosing random points (''x'', ''y'') in the square −1 < ''x'' < 1, −1 < ''y'' < 1 until : and then returning the required pair of normal s as : or, equivalently, : where and represent the cosine and |
Linear Congruential Generator
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation. The generator is defined by the recurrence relation: :X_ = \left( a X_n + c \right)\bmod m where X is the sequence of pseudo-random values, and : m,\, 0 |
Diehard Tests
The diehard tests are a battery of statistical tests for measuring the quality of a random number generator. They were developed by George Marsaglia over several years and first published in 1995 on a CD-ROM of random numbers. Test overview ; Birthday spacings : Choose random points on a large interval. The spacings between the points should be asymptotically exponentially distributed. The name is based on the birthday paradox. ; Overlapping permutations : Analyze sequences of five consecutive random numbers. The 120 possible orderings should occur with statistically equal probability. ; Ranks of matrices : Select some number of bits from some number of random numbers to form a matrix over , then determine the rank of the matrix. Count the ranks. ; Monkey tests : Treat sequences of some number of bits as "words". Count the overlapping words in a stream. The number of "words" that do not appear should follow a known distribution. The name is based on the infinite monkey theorem. ; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor Emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title the rank of the last office held". In some cases, the term is conferred automatically upon all persons who retire at a given rank, but in others, it remains a mark of distinguished service awarded selectively on retirement. It is also used when a person of distinction in a profession retires or hands over the position, enabling their former rank to be retained in their title, e.g., "professor emeritus". The term ''emeritus'' does not necessarily signify that a person has relinquished all the duties of their former position, and they may continue to exercise some of them. In the description of deceased professors emeritus listed at U.S. universities, the title ''emeritus'' is replaced by indicating the years of their appointmentsThe Protoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unimodal Distribution
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. Unimodal probability distribution In statistics, a unimodal probability distribution or unimodal distribution is a probability distribution which has a single peak. The term "mode" in this context refers to any peak of the distribution, not just to the strict definition of mode which is usual in statistics. If there is a single mode, the distribution function is called "unimodal". If it has more modes it is "bimodal" (2), "trimodal" (3), etc., or in general, "multimodal". Figure 1 illustrates normal distributions, which are unimodal. Other examples of unimodal distributions include Cauchy distribution, Student's ''t''-distribution, chi-squared distribution and exponential distribution. Among discrete distributions, the binomial distribution and Poisson distribution can be seen as unimodal, thou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ziggurat Algorithm
The ziggurat algorithm is an algorithm for pseudo-random number sampling. Belonging to the class of rejection sampling algorithms, it relies on an underlying source of uniformly-distributed random numbers, typically from a pseudo-random number generator, as well as precomputed tables. The algorithm is used to generate values from a monotonically decreasing probability distribution. It can also be applied to symmetric unimodal distributions, such as the normal distribution, by choosing a value from one half of the distribution and then randomly choosing which half the value is considered to have been drawn from. It was developed by George Marsaglia and others in the 1960s. A typical value produced by the algorithm only requires the generation of one random floating-point value and one random table index, followed by one table lookup, one multiply operation and one comparison. Sometimes (2.5% of the time, in the case of a normal or exponential distribution when using typical table ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mother (algorithm)
] A mother is the female parent of a child. A woman may be considered a mother by virtue of having given childbirth, birth, by raising a child who may or may not be her biological offspring, or by supplying her ovum for fertilisation in the case of gestational surrogacy. An adoptive mother is a female who has become the child's parent through the legal process of adoption. A biological mother is the female genetic contributor to the creation of the infant, through sexual intercourse or egg donation. A biological mother may have legal obligations to a child not raised by her, such as an obligation of monetary support. A putative mother is a female whose biological relationship to a child is alleged but has not been established. A stepmother is a woman who is married to a child's father and they may form a family unit, but who generally does not have the legal rights and responsibilities of a parent in relation to the child. A father is the male counterpart of a mother. Women who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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