Related papers: On $q$-Order Statistics
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
We present an argument about the origin of escort distributions used in conjunction with the q-entropy in non-additive thermo-statistics. The origin of the escort distributions is ascribed to the fact that the effective statistical…
The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function $\zeta(s)\equiv\sum_{n=1}^\infty…
We extend some results recently obtained by Dan Romik about the Taylor coefficients of the theta function $\theta_{3}\left(1\right)$ to the case $\theta_{3}\left(q\right)$ of an arbitrary value of the elliptic modulus $k.$ These results are…
Several generalizations of the logistic distribution, and certain related models, are proposed by many authors for modeling various random phenomena such as those encountered in data engineering, pattern recognition, and reliability…
The univariate quantile-quantile (Q-Q) plot is a well-known graphical tool for examining whether two data sets are generated from the same distribution or not. It is also used to determine how well a specified probability distribution fits…
This paper develops methods to study the distribution of Eulerian statistics defined by second-order recurrence relations. We define a random process to decompose the statistics over compositions of integers. It is shown that the numbers of…
Here, we leverage recent advances in information theory to develop a novel method to characterise the dominant character of the high-order dependencies of quantum systems. To this end, we introduce the Q-information: an…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the…
We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…
A novel approach to parton distributions parameterization in terms of quantum statistical functions is here outlined. The description, already proposed in previous publications, is here improved by adding to the statistical distributions an…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory.…
In earlier work generalizing a 1977 theorem of Alladi, the authors proved a partition-theoretic formula to compute arithmetic densities of certain subsets of the positive integers $\mathbb N$ as limiting values of $q$-series as $q\to \zeta$…
We show that the distribution function of the first particle in a discrete orthogonal polynomial ensemble can be obtained through a certain recurrence procedure, if the (difference or q-) log-derivative of the weight function is rational.…
In this paper some new characterizing theorems of exponential distribution based on order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved.
We show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system…
Since the pioneering work by Koenker and Bassett (1978), quantile regression models and its applications have become increasingly popular and important for research in many areas. In this paper, a random effects ordinal quantile regression…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…