Related papers: On $q$-Order Statistics
Here we suppose that the observed random variable has cumulative distribution function $F$ with regularly varying tail, i.e. $1-F \in RV_{-\alpha}$, $\alpha > 0$. Using the results about exponential order statistics we investigate…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
In this paper, a new exponential and logarithm related to the non-extensive statistical physics is proposed by using the q-sum and q-product which satisfy the distributivity. And we discuss the q-mapping from an ordinary probability to…
In this paper we analyze the probability distributions associated with rolling (possibly unfair) dice infinitely often. Specifically, given a $q$-sided die, if $x_i\in\{0,\ldots,q-1\}$ denotes the outcome of the $i^{\text{th}}$ toss, then…
We outline some simple prescriptions to define a distribution on the set $\mathbb{Q}_0$ of all the rational numbers in $[0,1]$, and we then explore both a few properties of these distributions, and the possibility of making these rational…
We study statistics on ordered set partitions whose generating functions are related to $p,q$-Stirling numbers of the second kind. The main purpose of this paper is to provide bijective proofs of all the conjectures of \stein…
In the present paper, we investigate special generalized q-Euler numbers and polynomials. Some earlier results of T. Kim in terms of q-Euler polynomials with weight alpha can be deduced. For presentation of our formulas we apply the method…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…
In this work, we prove the joint convergence in distribution of $q$ variables modulo one obtained as partial sums of a sequence of i.i.d. square integrable random variables multiplied by a common factor given by some function of an…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving…
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
In a recent article A.M. Kagan and G.J.Sz\'ekely introduced a notion of Q-independent and Q-identical distributed random variables. We give a complete description of polynomials which appear in these definitions.
We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…
The so called $q$-triplets were conjectured in 2004 and then found in nature in 2005. A relevant further step was achieved in 2005 when the possibility was advanced that they could reflect an entire infinite algebra based on combinations of…
Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We…
We define and study distributions in R^{d} that we call q-Normal. For q=1 they are really multidimensional Normal, for q\in(-1,1) they have densities, compact support and many properties that resemble properties of ordinary multidimensional…
We study semiorders induced by points drawn from a uniform random distribution. Of particular interest in this paper are the probabilities of generating specific semiorders and the equivalence classes they produce. We present a method for…
We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot…