Related papers: Tail universalities in rank distributions as an al…
We introduce $\zeta$- and $s$-values as quantile-based standardizations that are particularly suited for hypothesis testing. Unlike p-values, which express tail probabilities, $s$-values measure the number of semi-tail units into a…
We introduce the \textsc{Tailed-Uniform} proposal distribution for generating training simulations in simulation-based inference. Instead of sampling parameters uniformly within bounded regions, we extend the distribution beyond prior…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
Demographic parity (DP) is a widely studied fairness criterion in regression, enforcing independence between the predictions and sensitive attributes. However, constraining the entire distribution can degrade predictive accuracy and may be…
In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…
Decision-making problems of sequential nature, where decisions made in the past may have an impact on the future, are used to model many practically important applications. In some real-world applications, feedback about a decision is…
We study types that appear in ultraproducts that have distributions which can be thought of as a sequence of graphs. The property of having distributions that are captured by graphs is motivated by a commonality of $\mathrm{SOP}_2$-types…
The task of estimation of the tails of probability distributions having small samples seems to be still opened and almost unsolvable. The paper tries to make a step in filling this gap. In 2017 Jordanova et al. introduce six new…
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…
A central question in economics is whether automation will displace human labor and diminish standards of living. Whilst prior works typically frame this question as a competition between human labor and machines, we frame it as a…
This paper contains sharp estimates about the distribution of multiple random integrals of functions of several variables with respect to a normalized empirical measure, about the distribution of U-statistics and multiple Wiener-Ito…
Real-world visual data often exhibits a long-tailed distribution, where some ''head'' classes have a large number of samples, yet only a few samples are available for ''tail'' classes. Such imbalanced distribution causes a great challenge…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
The most well known probability distribution of probabilities is the Beta distribution. If we have observed $r$ `successes', each having a probability $\theta$, and $n-r$ `failures', each having a probability $1-\theta$. In this paper we…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large…
We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock…
This paper addresses the problem of estimating the tail index of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A…
Quantifying the similarity between symbolic sequences is a traditional problem in Information Theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to…
Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers…