Related papers: Three competing patterns
We treat success runs of independent identically distributed Bernoulli trials (with success parameter $p$) distributed according to the Type II binomial distribution of order $k$. However, the success runs are separated by a gap $g\ge1$ (a…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
Let $A^{(n)}_{l;k}\subset S_n$ denote the set of permutations of $[n]$ for which the set of $l$ consecutive numbers $\{k, k+1,\cdots, k+l-1\}$ appears in a set of consecutive positions. Under the uniformly probability measure $P_n$ on…
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out…
We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important…
In this paper we study the problem of making predictions using multiple structural casual models defined by different agents, under the constraint that the prediction satisfies the criterion of counterfactual fairness. Relying on the…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
For three natural classes of dynamic decision problems; 1. additively separable problems, 2. discounted problems, and 3. discounted problems for a fixed discount factor; we provide necessary and sufficient conditions for one sequential…
In this note we study the {\em asymptotic popularity}, that is, the limit probability to find a given consecutive pattern at a random position in a random permutation in the eighteen classes of permutations avoiding at least two length 3…
Many classification models produce a probability distribution as the outcome of a prediction. This information is generally compressed down to the single class with the highest associated probability. In this paper, we argue that part of…
In this paper a way is suggested for calculating the probability of consecutive number strings within a sequence of n numbers randomly drawn (without replacement) among the set of the first N consecutive numbers, with N>>n. An explicit…
Cerny's conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping…
A new unequal probability sampling method is proposed. This method is sequential. The decision to select or not each unit is made based on the order in which the units appear. A variant of this method allows selecting a sample from a…
We study additive properties of consecutive prime numbers and the primality of the sums they generate. For a given prime number $p_n$, we consider the sums \[ S_k(p_n) = p_n + p_{n+1} + \cdots + p_{n+k-1}, \] where $k \ge 3$ is an odd…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…
How should dispersal strategies be chosen to increase the likelihood of survival of a species? We obtain the answer for the spatially extended versions of three well-known models of two competing species with unequal diffusivities. Though…
Assuming a uniform $q$-variant of the prime $k$-tuple conjecture, we compute moments of the number of primes in arithmetic progressions to a large modulus $q$ as the residue classes vary. Consequently, depending on the size of $\varphi(q)$,…
We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…
In real world social networks, there are multiple cascades which are rarely independent. They usually compete or cooperate with each other. Motivated by the reinforcement theory in sociology we leverage the fact that adoption of a user to…