Generalizations of distributions related to ( $$k_1,k_2$$ k 1 , k 2 )-runs

ON NEGATIVE BINOMIAL APPROXIMATION TO k-RUNS

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suita...

Survey of Discrete Distributions of Order k and Related Distributions

The distribution of the number of trials until the first occurrence of consecutive k successes in Bernoulli trials with success probability p is called a geometric distribution of order k. This definition is due to Philippou, Georghiou and Philippou (1983). Though the distribution seems to have been interested since De Moivre (1667-1754)’s works (Todhunter (1865), Feller (1968), Johnson, Kotz a...

Turán densities of some hypergraphs related to K k k + 1 ∗

Department of Mathematics, University of Illinois, 1409 W. Green Street Urbana, IL 61801, [email protected] Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, [email protected] Trinity College, Cambridge CB2 1TQ England, [email protected] Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA. 4 Department of Mathemat...

Algorithm Sum of Densities Average Cases K = 2 K = 3 K = 4 K = 8 K = 1 0 K = 1 5 K = 2 0 Improvement

Top-down partitioning has focused on minimum cut or ratio cut objectives, while bottom-up clustering has focused on density-based objectives. In seeking a more uni ed perspective, we propose a new sum of densities measure for multi-way circuit decomposition, where the density of a subhypergraph is the ratio of the number of edges to the number of nodes in the subhypergraph. Finding a k-way part...

IMAGINARY QUADRATIC FIELDS k WITH Cl2(k) ≃ (2, 2 m) AND RANK Cl2(k 1) = 2