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  • 1
    Electronic Resource
    Electronic Resource
    An exact determination of serial correlations of pseudo-random numbers (1971)
    Springer
    Numerische Mathematik 17 (1971), S. 101-123 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Exact expressions for serial correlations of sequences of pseudo-random numbers are derived. The reduction to generalized Dedekind sums is of optimum simplicity and covers all cases of the linear congruential method. The subsequent evaluation of the generalized Dedekind sums is based on a modified Euclidean algorithm whose quotients are recognized as the main contributors to the size of the serial correlations. This leads to the establishment of bounds as well as of fast computer programs. Moreover, some light is thrown upon the general question of quality in random number generation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01406000
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A combinatorial method for the generation of normally distributed random numbers (1973)
    Springer
    Computing 11 (1973), S. 137-146 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Methode erzeugt Zufallszahlen der standardisierten Normalverteilung. Für das Zentrum $$|x| \leqslant \sqrt 2 $$ (84,27% aller Fälle) wird eine Variante des v.Neumannschen Vergleichsverfahrens zur Erzeugung exponentialverteilter Zufallszahlen vorgeschlagen. Für die Werte $$|x| 〉 \sqrt 2 $$ der Normalverteilung wird eine Verwerfungsmethode vonG. Marsaglia verwendet, bei der die majorisierende Funktion die Exponentialfunktion ist. Die dafür benötigten exponential-verteilten Zufallszahlen werden durch die ursprüngliche v.Neumann'sche Methode erzeugt.
    Notes: Abstract The proposed method generates standard normal variablesx. In 84.27% of all cases sampling from the centre $$(|x| \leqslant \sqrt 2 )$$ of the normal distribution is carried out using a variant ofJ. v. Neumann's algorithm for the generation of exponentially distributed random numbers. For sampling from the tails $$(|x| 〉 \sqrt 2 )$$ the same method byJ. v. Neumann is combined with an acceptance-rejection approach ofG. Marsaglia.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02252903
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Pseudo-random numbers (1970)
    Springer
    Computing 6 (1970), S. 121-138 
    Details
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Man erzeugt meist Zufallszahlen auf multiplikativem Wege: Ausgehend von einer ganzen Zahly o konstruiert man eine Folge ganzer Zahlen {y i} durchy i+1эa y i (mod 2k). Die Brüchex i=y i /2 k sind die gewünschten Zufallszahlen im Intervall (0,1). Die Autoren schlagen 4a ≈2k ξ für die Wahl des Faktors vor. Dabei ist $$\xi = \frac{1}{2}(\sqrt 5 - 1)$$ die Zahl des Goldenen Schnittes. Dieser Faktor erzwingt statistische Fast-Unabhängigkeit zwischenx i undx i+1. Darüberhinaus werden Abschätzungen für die Autokorrelation von zwei Zufallszahlen hergeleitet, die die gleiche Größenordnung haben, wieGreenbergers Abschätzung für die Wahl $$a \approx \sqrt {2^k }$$ . Die exakten Werte der Autokorrelation fürk≤100 zeigen, daß der Faktor 4a ≈2k ξ vorzuziehen ist. Eine Million Zufallszahlen einer speziellen Serie wurden statistischen Tests unterworfen. Die ALGOL- und FORTRAN-Programme sind für den praktischen Gebrauch dieser Arbeit bestimmt.
    Notes: Summary Pseudo-random numbers are usually generated by multiplicative methods. For binary computers the sequencesy i+1эa y i (mod 2k) are common and the derived numbersx i=y i/2k are taken as samples from the uniform distribution in (0, 1). In this paper 4a ≈2k ξ is proposed as a guide line for the choice of the multiplicatora where ξ is the golden section number $$\frac{1}{2}(\sqrt 5 - 1)$$ . Such values of the factor a have the property that an approximate knowledge ofy i will not yield information about the successory i+1. Bounds for the autocorrelations of the entire sequences are derived. These are of the same order of magnitude asGreenberger's bounds in the case $$a \approx \sqrt {2^k }$$ . However, the precise evaluation of the serial correlations fork≤100 indicates that the factors 4a ≈2k ξ are superior. One million numbers of a special sequence were tested statistically. The included ALGOL and FORTRAN subroutines will enable programmers to make practical use of this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02241740
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  • 4
    Electronic Resource
    Electronic Resource
    Computer methods for sampling from gamma, beta, poisson and bionomial distributions (1974)
    Springer
    Computing 12 (1974), S. 223-246 
    Details
    ISSN: 1436-5057
    Keywords: Random numbers ; pseudorandom ; normal distribution ; gamma distribution ; bei distribution ; Poisson distribution ; binomial distribution ; simulation ; numerical analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur Erzeugung nicht-gleichverteilter Zufallszahlen braucht man Methoden, die gleichverteilte Zufallszahlen in Größen der gegebenen Verteilung transformieren. Es werden Transformationen untersucht, die Gamma-, Beta-, Poisson- oder Binomial-verteilte Zufallszahlen produzieren. Approximative Verfahren werden nicht behandelt. Die bisher bekannten Algorithmen sind langsam, wenn die Parameter der Verteilungen groß sind. Daher werden neue Methoden eingeführt, die diesen Nachteil weitgehend vermeiden. In allen Verfahren dürfen die Parameter beliebig und jedesmal neu gewählt werden. Für manche Transformationen werden normalverteilte Zufallszahlen als Zwischenschritt benötigt; die hierfür verwendete Methode ist ebenfalls angegeben.
    Notes: Abstract Accurate computer methods are evaluated which transform uniformly distributed random numbers into quantities that follow gamma, beta, Poisson, binomial and negative-binomial distributions. All algorithms are designed for variable parameters. The known convenient methods are slow when the parameters are large. Therefore new procedures are introduced which can cope efficiently with parameters of all sizes. Some algorithms require sampling from the normal distribution as an intermediate step. In the reported computer experiments the normal deviates were obtained from a recent method which is also described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02293108
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Vergleichende tierexperimentelle Untersuchungen zur Effektivität verschiedener endokriner Behandlungsmethoden beim hormonabhängigen Mammacarcinom (1973)
    Springer
    Archives of gynecology and obstetrics 214 (1973), S. 296-297 
    Details
    ISSN: 1432-0711
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00671149
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  • 6
    Electronic Resource
    Electronic Resource
    Eine experimentelle Anordnung zur Photonenstreuung unterhalb 140 MeV (1971)
    Springer
    The European physical journal 241 (1971), S. 166-178 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The facilities for photon scattering experiments at the Mainz electron linear accelerator are described. They include an energy analyzing system, the bremsstrahlung target and a photon spectrometer (NaI-crystals). The question of background elimination is discussed. The scattered photon spectrum from a carbon target is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01397905
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    Paper (German National Licenses)
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