Strong limit theorems in the multi-color generalized allocation scheme

The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers of balls.Comment: 11 page

Limit theorems for runs containing two types of contaminations. Paper with detailed proofs

In this paper, sequences of trials having three outcomes are studied. The outcomes are labelled as success, failure of type I and failure of type II. A run is called at most 1+1 contaminated, if it contains at most 1 failure of type I and at most 1 failure of type II. The limiting distribution of the first hitting time and the accompanying distribution for the length of the longest at most 1+1 contaminated run are obtained. This paper contains the detailed mathematical proofs. Simulation results supporting the theorems are also presented.Comment: 25 pages, 8 figure

Convergence rate for the longest T-contaminated runs of heads. Paper with detailed proofs

We study the length of $T$-contaminated runs of heads in the well-known coin tossing experiment. A $T$-contaminated run of heads is a sequence of consecutive heads interrupted by $T$ tails. For $T=1$ and $T=2$ we find the asymptotic distribution for the first hitting time of the $T$ contaminated run of heads having length $m$; furthermore, we obtain a limit theorem for the length of the longest $T$-contaminated head run. We prove that the rate of the approximation of our accompanying distribution for the length of the longest $T$-contaminated head run is considerably better than the previous ones. For the proof we use a powerful lemma by Cs\'aki, F\"oldes and Koml\'os.Comment: 20 pages, 4 figure

Corruption manual for beginners: "Corruption techniques" in public procurement with examples from Hungary

This paper develops 30 novel quantitative indicators of grand corruption that operationalize 20 distinct techniques of corruption in the context of public procurement. Each indicator rests on a thorough qualitative understanding of rent extraction from public contracts by corrupt networks as evidenced by academic literature, interviews and media content analysis. Feasibility and usefulness of the proposed indicators are demonstrated using micro-level public procurement data from Hungary in 2009-2012. While the prime value of this broad set of indicators is the possibility of combining them into a robust composite indicator of high-level corruption, the high degree of detail also reveals that many regulatory interventions have succeeded in changing the form of corruption, but not its overall incidence