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- 1
-
M.S. Ali and S.D. Silvey.
A general class of coefficients of divergence of one distribution
from another.
J. Roy. Statist. Soc., Ser B(28):131-142, 1966.
- 2
-
N. S. Altman.
Bit-wise behavior of random number generators.
SIAM J. Sci. Stat. Comput., 9(5):941-949, 1988.
- 3
-
P. Billingsley.
Probability and Measure.
Wiley and Sons, New York, second edition, 1986.
- 4
-
D.E. Boekee.
A generalization of the Fisher information measure.
Delft University Press, Delft, 1977.
- 5
-
P. Bratley, B. Fox, and L.E. Schrage.
A Guide to Simulation.
Springer-Verlag, New York, 1983.
- 6
-
M. Brunner.
Anwendungen der Risikomengentechnik zum Beweis von
Konvergenzsätzen für Markovketten.
PhD thesis, Universität Salzburg, Österreich, 1988.
- 7
-
N. Cressie and T. Read.
Multinomial Goodness-of-fit Tests.
J. R. Statist. Soc. B, 46(3):440-464, 1984.
- 8
-
I. Csiszár.
Eine informationstheoretische Ungleichung und ihre Anwendung auf
den Beweis der Ergodizität von Markoffschen Ketten.
Magyar Tud. Akad. Mat. Kutató Int. Közl, 8:85-108,
1963.
- 9
-
J. Eichenauer-Herrmann.
Statistical independence of a new class of inversive congruential
pseudorandom numbers.
Math. Comp., 60:375-384, 1993.
- 10
-
J. Eichenauer-Herrmann, E. Herrmann, and S. Wegenkittl.
A survey of quadratic and inversive congruential pseudorandom
numbers.
In H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof,
editors, Monte Carlo and Quasi-Monte Carlo Methods 1996, number 127 in
Lecture Notes in Statistics, pages 66-97. Springer, New York, 1997.
- 11
-
K. Entacher and S. Wegenkittl.
The PLAB picturebook: Load tests and ultimate load tests,
part II: Subsequences.
Report no. 2, PLAB - reports, University of Salzburg, 1997.
Available on the internet at
http://random.mat.sbg.ac.at/team/.
- 12
-
G. S. Fishman.
Multiplicative congruential random number generators with modulus
:
An exhaustive analysis for
and a partial analysis for
.
Mathematics of Computation, 54:331-344, 1990.
- 13
-
G. S. Fishman and L. R. Moore.
A statistical evaluation of multiplicative congruential random number
generators with modulus 231-1.
Journal of the American Statistical Association, 77:129-136, 1982.
- 14
-
G.S. Fishman and L.R. Moore.
An exhaustive analysis of multiplicative congruential random number
generators with modulus 231-1.
SIAM J. Sci. Statist. Comput., 7:24-45, 1986.
see also the Erratum, ibib. 7(1986), p. 1058.
- 15
-
M. Flahive and H. Niederreiter.
On inversive congruential generators for pseudorandom numbers.
In G.L. Mullen and P.J.-S. Shiue, editors, Finite Fields, Coding
Theory, and Advances in Communications and Computing, pages 75-80. Dekker,
New York, 1992.
- 16
-
I. J. Good.
The serial test for sampling numbers and other tests for randomness.
Proc. Cambridge Philosophical Society, 49:276-284, 1953.
- 17
-
J. Hartung, B. Elpelt, and K. H. Klösener.
Statistik.
R. Oldenburg, Munich, 9th edition, 1993.
- 18
-
P. Hellekalek.
Inversive pseudorandom number generators: concepts, results, and
links.
In C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman, editors,
Proceedings of the 1995 Winter Simulation Conference, pages 255-262.
IEEE Press, Piscataway, N.J., 1995.
- 19
-
P. Hellekalek.
Good random number generators are (not so) easy to find.
to appear in Mathematics and Computers in Simulation, 1998.
- 20
-
A. B. Israel and T. Greville.
Generalized Inverses: Theory and Applications.
Wiley Interscience Publications. Wiley and Sons, New York, 1974.
- 21
-
K. Jacobs.
Markov-Prozesse mit endlich vielen Zuständen.
Heidelberger Taschenbücher 98, Selecta Mathematica IV.
Springer Verlag, 1972.
- 22
-
P. Kafka, F. Österreicher, and I. Vincze.
On powers of f-divergences defining a distance.
Studia Sci. Math. Hungar., 26:415-422, 1991.
- 23
-
S. Karlin.
A second course in stochastic processes.
Academic Press, London, 1991.
- 24
-
S. Kotz et al., editors.
Minimum discrimination information (MDI) estimation,
volume 5 of Wiley Interscience Publication, pages 527-529.
John Wiley, 1985.
- 25
-
S. Kullback.
Information Theory and Statistics.
John Wiley, New York, 1959.
- 26
-
S. Kullback and R. Leibler.
On information and sufficiency.
Ann. Math. Statist., 22:79-86, 1951.
- 27
-
L. Le Cam.
Asymptotic Methods in Statistical Decision Theory.
Springer, New York, 1986.
- 28
-
P. L'Ecuyer.
Efficient and portable combined random number generators.
Comm. ACM, 31(6):742-774, 1988.
- 29
-
P. L'Ecuyer, J.F. Cordeau, and R. Simard.
Close-points spatial tests for random number generators.
Submitted for publication, 1997.
- 30
-
H. Leeb and S. Wegenkittl.
Inversive and linear congruential pseudorandom number generators in
empirical tests.
ACM Trans. Modeling and Computer Simulation, 7:272-286,
1997.
- 31
-
F. Liese and I. Vajda.
Markov-Prozesse mit endlich vielen Zuständen.
Teubner-Texte zur Mathematik, Band 95. Teubner, 1987.
- 32
-
G. Marsaglia.
A current view of random number generators.
In L. Billard, editor, Computer Science and Statistics: The
Interface, pages 3-10. Elsevier Science Publishers B.V., 1985.
- 33
-
M. Matsumoto and Y. Kurita.
Twisted GFSR Generators.
ACM Trans. Model. Comput. Simul., 2(3):179-194, 1992.
- 34
-
M. Matsumoto and Y. Kurita.
Twisted GFSR generators II.
ACM Trans. Model. Comput. Simul., 4:254-266, 1994.
- 35
-
K. Matusita.
Decision rules based on the distance for problems of fit.
Ann. Math. Statist., 26:631-640, 1955.
- 36
-
S. P. Meyn and R. L. Tweedie.
Markov Chains and Stochastic Stability.
Springer, London, 1993.
- 37
-
M. Z. Nashed, editor.
Generalized Inverses and Applications, New York, 1976. Academic
Press.
- 38
-
J. Neyman.
Contributions to the theory of the
test.
Proceedings of the First Berkley Symposium on Mathematical Statistics
and Probability, 1949.
- 39
-
H. Niederreiter.
Random Number Generation and Quasi-Monte Carlo Methods.
SIAM, Philadelphia, USA, 1992.
- 40
-
H. Niederreiter.
On a new class of pseudorandom numbers for simulation methods.
J. Comput. Appl. Math., 56:159-167, 1994.
- 41
-
H. Niederreiter.
New developments in uniform pseudorandom number and vector
generation.
In H. Niederreiter and P. Jau-Shyong Shiue, editors, Monte Carlo and Quasi-Monte Carlo Methods in Scientific
Computing, volume 106 of Lecture Notes in Statistics.
Springer, 1995.
- 42
-
S. Orey.
An ergodic theorem for Markov chains.
Z. W-theorie verw. Gebiete, pages 174-176, 1962.
- 43
-
F. Österreicher.
The construction of least favourable distributions is traceable to a
minimal perimeter problem.
Studia Sci. Math. Hungar., 17:341-351, 1982.
- 44
-
F. Österreicher and I. Vajda.
A new class of metric divergences on probability spaces and its
statistical applications, 1997.
submitted.
- 45
-
K. Pearson.
Philos. Mag, Set. 5, 50: 157-175, 1900.
- 46
-
O. E. Percus and P. A. Whitlock.
Theory and Application of Marsaglia's Monkey Test for
Pseudorandom Number Generators.
ACM Transactions on Modeling and Computer Simulation, 5
(2):87-100, 1995.
- 47
-
C. R. Rao and S. K. Mitra.
Generalized Inverse of Matrices and its Applications.
Wiley Series in Probability and Mathematical Statistics. Wiley and
Sons, 1971.
- 48
-
T. Read and N. Cressie.
Goodness-of-Fit Statistics for Discrete Multivariate Data.
Springer Series in Statistics. Springer Verlag, New York, 1988.
- 49
-
V. Romanovsky.
Discrete Markov Chains.
Wolters-Noordhoff Publishing, Groningen, Netherlands, 1970.
- 50
-
E. Seneta.
Non-negative matrices and Markov chains.
Springer Series in Statistics. Springer, New York, second edition,
1981.
- 51
-
E. Stadlober and R. Kremer.
Sampling from discrete and continuous distributions with c-Rand.
In G. Pflug and U. Dieter, editors, Simulation and
Optimization, volume 374 of Lecture Notes in Economics and
Math. Systems, pages 154-162. Springer-Verlag, Berlin, 1992.
- 52
-
E. Stadlober and F. Niederl.
C-Rand: a package for generating nonuniform random variates.
In Compstat '94, Software Descriptions, pages 63-64, 1994.
- 53
-
I. Vattulainen, T. Ala-Nissila, and K. Kankaala.
Physical models as tests of randomness.
Physical Review E, 52(3):3205-3213, 1995.
- 54
-
I. Vincze.
On the concept and measure of information contained in an
observation.
In J. Gani and V.F. Rohatgi, editors, Contributions to
Probability, pages 207-214. Academic Press, 1981.
- 55
-
S. Wegenkittl.
Empirical testing of pseudorandom number generators.
Master's thesis, Universität Salzburg, Österreich, 1995.
Available on the internet at
http://random.mat.sbg.ac.at/team/.
- 56
-
S. Wegenkittl.
The PLAB picturebook: Load tests and ultimate load tests,
part I.
Report no. 1, PLAB - reports, University of Salzburg, 1997.
Available on the internet at
http://random.mat.sbg.ac.at/team/.
Stefan Wegenkittl
1998-05-19