Related papers: Universality in movie rating distributions
One of the most puzzling properties of observed galaxies is the universality of the empirical correlation between the star formation rate and average gas surface density on kiloparsec scales (the Schmidt law). In this study I present…
We consider the distribution of the major index on standard tableaux of arbitrary straight shape and certain skew shapes. We use cumulants to classify all possible limit laws for any sequence of such shapes in terms of a simple auxiliary…
A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal,…
Normality is the most often mathematical supposition used in data modeling. Nonetheless, even based on the law of large numbers (LLN), normality is a strong presumption given that the presence of asymmetry and multi-modality in real-world…
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…
We give lower bounds on the maximum possible girth of an $r$-uniform, $d$-regular hypergraph with at most $n$ vertices, using the definition of a hypergraph cycle due to Berge. These differ from the trivial upper bound by an absolute…
The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different…
We introduce a simple model to study movie competition in the recommender systems. Movies of heterogeneous quality compete against each other through viewers' reviews and generate interesting dynamics of box-office. By assuming mean-field…
The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…
We consider the problem of classifying documents not by topic, but by overall sentiment, e.g., determining whether a review is positive or negative. Using movie reviews as data, we find that standard machine learning techniques definitively…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
The Internet Movie Database (IMDb) is one of the most-visited websites in the world and the premier source for information on films. Like Wikipedia, much of IMDb's information is user contributed. IMDb also allows users to voice their…
Given a random process $x(\tau)$ which undergoes stochastic resetting at a constant rate $r$ to a position drawn from a distribution ${\cal P}(x)$, we consider a sequence of dynamical observables $A_1, \dots, A_n$ associated to the…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
Assessment of multimedia quality relies heavily on subjective assessment, and is typically done by human subjects in the form of preferences or continuous ratings. Such data is crucial for analysis of different multimedia processing…
We analyze the dynamics of pattern forming fronts which propagate into an unstable state, and whose dynamics is of the pulled type, so that their asymptotic speed is equal to the linear spreading speed v^*. We discuss a method that allows…
This article presents an important theorem, which shows that from the moments of the standard normal distribution one can generate density functions originating a family of models. Additionally, we discussed that different random variable…
We estimate up to universal constants tails of symmetric and totally asymmetric 1-dimensional $\alpha$-stable distributions in terms of functions of the parameters of these distributions. In particular, for values of $\alpha$ close to $2$…
Three conjectures from [R. Hegselmann, The Journal of Artificial Societies and Social Simulations 26(4), 11 (2023)] about the Hegselmann-Krause opinion dynamics and the structure of $\epsilon$-switches are proved. The first conjecture…