On the birthday problem: Some generalizations and applications.
On the connection between cherry-tree copulas and truncated R-vine copulas
Vine copulas are a flexible way for modeling dependences using only pair-copulas as building blocks. However if the number of variables grows the problem gets fastly intractable. For dealing with this problem Brechmann at al. proposed the truncated R-vine copulas. The truncated R-vine copula has the very useful property that it can be constructed by using only pair-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this...
On the distribution of depths in increasing trees.
On the distribution of waiting time until k-th repetition of any event.
On the height of a random set of points in a -dimensional unit cube.
On the joint entropy of -wise-independent variables
How low can the joint entropy of -wise independent (for ) discrete random variables be, subject to given constraints on the individual distributions (say, no value may be taken by a variable with probability greater than , for )? This question has been posed and partially answered in a recent work of Babai [Entropy versus pairwise independence (preliminary version),...
On the local time density of the reflecting Brownian bridge.
On the lower bound of the spectral norm of symmetric random matrices with independent entries.
On the Newcomb-Benford law in models of statistical data.
We consider positive real valued random data X with the decadic representation X = Σi=∞∞Di 10i and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = Di ≥ 1, Di+1 = Di+2 = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log10(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with log10X uniformly distributed on an interval (m,n) where m and n are integers. We show that if log10X has a distribution function...
On the number of word occurrences in a semi-Markov sequence of letters
Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.
On the shuffling algorithm for domino tilings.
On the size of a maximal induced tree in a random graph
On useful schema in survival analysis after heart attack
Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers
One-dimensional random walks, decreasing rearrangements and discrete Steiner symmetrization
Orthogonal polynomial ensembles in probability theory.