The integral limit theorem in the first passage problem for sums of independent nonnegative lattice variables.
Virchenko, Yuri P., Yastrubenko, M.I. (2006)
Abstract and Applied Analysis
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Virchenko, Yuri P., Yastrubenko, M.I. (2006)
Abstract and Applied Analysis
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Mitzenmacher, M., Oliveira, R., Spencer, J. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Minkova, Leda D. (2004)
Journal of Applied Mathematics and Stochastic Analysis
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Mostafa K. Ardakani, Shaun S. Wulff (2014)
Discussiones Mathematicae Probability and Statistics
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Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by...
Căbulea, Lucia (2001)
Acta Universitatis Apulensis. Mathematics - Informatics
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M. Fisz (1955)
Studia Mathematica
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B. Kopociński (2004)
Applicationes Mathematicae
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We define two splitting procedures of the interval [0,1], one using uniformly distributed points on the chosen piece and the other splitting a piece in half. We also define two procedures for choosing the piece to be split; one chooses a piece with a probability proportional to its length and the other chooses each piece with equal probability. We analyse the probability distribution of the lengths of the pieces arising from these procedures.
Oldřich Kropáč (1982)
Aplikace matematiky
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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types and are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and...