Related papers: A Characterization Based On Products of Order Stat…
As input data distributions evolve, the predictive performance of machine learning models tends to deteriorate. In practice, new input data tend to come without target labels. Then, state-of-the-art techniques model input data distributions…
Statistical mechanics provides a useful analog for understanding the behavior of complex adaptive systems, including electric power markets and the power systems they intend to govern. Market-based control is founded on the conjecture that…
We show that when Bjorken $x_B$ is large, the leading order twist-four contributions to the structure functions can be expressed in terms of the derivatives of the normal twist-two parton distributions. Our analytical results are not only…
In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In…
We introduce a novel perspective by linking ordered probabilistic choice to copula theory, a mathematical framework for modeling dependencies in multivariate distributions. Each representation of ordered probabilistic choice behavior can be…
Available in the literature are properties which characterize the gamma distribution via independence of two appropriately chosen statistics. Well-known is the classical result when one of the statistics is the sample mean and the other one…
The statistical properties of a stochastic process may be described (1)by the expectation values of the observables, (2)by the probability distribution functions or (3)by probability measures on path space. Here an analysis of level (3) is…
The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of experiments in applied statistics. In this paper we study some…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
We present a new method to extract parton distribution functions from high energy experimental data based on a specific type of neural networks, the Self-Organizing Maps. We illustrate the features of our new procedure that are particularly…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
A field theory is built for self-similar statistical systems with both generating functional being the Mellin transform of the Tsallis exponential and generator of the scale transformation that is reduced to the Jackson derivative. With…
The main goal of this article is to introduce new quantitative characteristics of cycles in finite simple connected graphs and to establish relations of these characteristics with the stretch and spanning tree congestion of graphs. The main…
Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law…
In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums.…
We present a streamlined proof (and some refinements) of a characterization (due to F. Carlson and G. Bourion, and also to P. Erd\"os and H. Fried) of the so called Szeg\"o's power series. This characterization is then applied to readily…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason…
We propose new classes of tests for the Pareto type I distribution using the empirical characteristic function. These tests are $U$ and $V$ statistics based on a characterisation of the Pareto distribution involving the distribution of the…