Related papers: Run and Frequency quotas for q-binary trials
The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A…
The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution (2) the testing data distribution. Although these two distributions are identical and identifiable when…
In this work, we explore both the ordinary $q$-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the $q$-deformed diffusion differential equation. This…
The quantum random walk has been much studied recently, largely due to its highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum walk on the line: the presence of decoherence…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
We offer a simple analysis of the problem of choosing a statistical experiment to optimize the induced distribution of posterior medians, or more generally $q$-quantiles for any $q \in (0,1)$. We show that all implementable distributions of…
We propose a new Q-learning variant, called 2RA Q-learning, that addresses some weaknesses of existing Q-learning methods in a principled manner. One such weakness is an underlying estimation bias which cannot be controlled and often…
The challenge of simulating random variables is a central problem in Statistics and Machine Learning. Given a tractable proposal distribution $P$, from which we can draw exact samples, and a target distribution $Q$ which is absolutely…
In this paper we provide formulas for the expectation of a conditional game duration in a finite state-space one-dimensional gambler's ruin problem with arbitrary winning $p(n)$ and losing $q(n)$ probabilities (i.e., they depend on the…
We compare different approximations for the wait time in distribution networks, in which all warehouses use an (R,Q)-order policy. Reporting on the results of extensive computational experiments, we evaluate the quality of several…
We introduce a new permutation statistic, namely, the number of cycles of length $q$ consisting of consecutive integers, and consider the distribution of this statistic among the permutations of $\{1,2,...,n\}$. We determine explicit…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The…
For a prime $p\ge 5$ let $q_0,q_1,\ldots,q_{(p-3)/2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p-3)/2$-periodic binary sequences $(d_n)$ and $(t_n)$ defined by $d_n=q_n+q_{n+1}\bmod 2$ and $t_n=1$ if…
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…
Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of…
Quantum theory (QT) provides statistical predictions for various physical phenomena. The outcomes of these measurements are in general some numerical time series registered by some macroscopic instruments. The various empirical probability…
In this paper, we investigate the trinomial probability distribution of the first and second kind from the $\mathcal{R}(p,q)$-quantum algebras. Moreover, we compute their $\mathcal{R}(p,q)$-factorial moments and derive the corresponding…
Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to…
We characterise the probability distributions that arise from quantum circuits all of whose gates commute, and show when these distributions can be classically simulated efficiently. We consider also marginal distributions and the…