Displaying similar documents to “On the birthday problem: Some generalizations and applications.”

Some properties and applications of probability distributions based on MacDonald function

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 x n K n ( x ) , x 0 , x n K n ( x x ) , x 𝐑 and x n + 1 K n ( x ) , x 0 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...

Random split of the interval [0,1]

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.