Math

Physics Maths Engineering

Heavy-Tailed Probability Distributions: Some Examples of Their Appearance

Lev B. Klebanov,

Lev B. Klebanov

Institution: Department of Probability and Mathematical Statistics, Charles University, 186 75 Prague, Czech Republic

Email:

Yulia V. Kuvaeva-Gudoshnikova,

Yulia V. Kuvaeva-Gudoshnikova

Institution: Department of Finance, Money Circulation and Credit, Ural State University of Economics, 620144 Yekaterinburg, Russia

Email:

Svetlozar T. Rachev

Svetlozar T. Rachev

Institution: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA

Email:


We provide two examples of the appearance of heavy-tailed distributions in social sciences applications. Among these distributions are the laws of Pareto and Lotka and some new ones. The examples are illustrated through the construction of suitable toy models.

Physics Maths Engineering

Sequential Test of Fuzzy Hypotheses

Mohammad Ghasem Akbari

Mohammad Ghasem Akbari

Institution:

Email:


This paper explores the problem of testing statistical hypotheses when the hypotheses are fuzzy and the data are crisp. The authors introduce new definitions for mass (density) probability functions with fuzzy parameters, as well as probabilities of type I and type II errors. They then present and prove a sequential probability ratio test for fuzzy hypotheses based on these new error definitions. ...
1 month ago

Physics Maths Engineering

Inverse problem for semilinear wave equation with strong damping

Nataliya Protsakh

Nataliya Protsakh

Institution:

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The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using a...
2 months ago

Physics Maths Engineering

Regression with Ordered Predictors via Ordinal Smoothing Splines

Nathaniel E. Helwig

Nathaniel E. Helwig

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The article "Regression with Ordered Predictors via Ordinal Smoothing Splines" by Nathaniel E. Helwig addresses the challenges of incorporating ordered categorical predictors into regression models. Traditional regression frameworks often treat ordinal predictors as either nominal (unordered) or continuous variables, which can be theoretically and computationally undesirable. This study propose...
2 months ago

Physics Maths Engineering

A Tree-Based Multiscale Regression Method

Haiyan Cai,

Haiyan Cai

Institution:

Email:

Qingtang Jiang

Qingtang Jiang

Institution:

Email:


The article "A Tree-Based Multiscale Regression Method" by Haiyan Cai and Qingtang Jiang introduces a novel regression technique designed to effectively handle high-dimensional data. This method adapts to the intrinsic lower-dimensional structure of the data, mitigating the challenges posed by the "curse of dimensionality." It also offers smoother estimates in regions where the regression funct...
2 months ago

Physics Maths Engineering

CPD-Structured Multivariate Polynomial Optimization

Muzaffer Ayvaz,

Muzaffer Ayvaz

Institution:

Email:

Lieven De Lathauwer

Lieven De Lathauwer

Institution:

Email:


We introduce the Tensor-Based Multivariate Optimization (TeMPO) framework for use in nonlinear optimization problems commonly encountered in signal processing, machine learning, and artificial intelligence. Within our framework, we model nonlinear relations by a multivariate polynomial that can be represented by low-rank symmetric tensors (multi-indexed arrays), making a compromise between model g...
2 months ago

Physics Maths Engineering

Three little arbitrage theorems

Mauricio Contreras G.,

Mauricio Contreras G.

Institution:

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Roberto Ortiz H.

Roberto Ortiz H.

Institution:

Email:


The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation wi...
2 months ago

Physics Maths Engineering

Kernel-Based Analysis of Massive Data

Hrushikesh N. Mhaskar

Hrushikesh N. Mhaskar

Institution:

Email:


The article "Kernel-Based Analysis of Massive Data" by Hrushikesh N. Mhaskar, published in Frontiers in Applied Mathematics and Statistics in October 2020, addresses the challenges of analyzing large datasets using kernel-based methods. Source

Physics Maths Engineering

Mean-ETL Optimization in HorseRace Competition

Barret P. Shao

Barret P. Shao

Institution:

Email:


This article explores the application of a new portfolio optimization approach called Mean-ETL (Mean-Expected Tail Loss). This method combines traditional mean return and the risk measure of expected tail loss to create more balanced portfolios that account for both returns and risks, particularly in the context of financial markets. The study demonstrates the practical implementation of Mean-E...
2 months ago

Physics Maths Engineering

Heavy-Tailed Probability Distributions: Some Examples of Their Appearance

Lev B. Klebanov,

Lev B. Klebanov

Institution: Department of Probability and Mathematical Statistics, Charles University, 186 75 Prague, Czech Republic

Email:

Yulia V. Kuvaeva-Gudoshnikova,

Yulia V. Kuvaeva-Gudoshnikova

Institution: Department of Finance, Money Circulation and Credit, Ural State University of Economics, 620144 Yekaterinburg, Russia

Email:

Svetlozar T. Rachev

Svetlozar T. Rachev

Institution: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA

Email:


We provide two examples of the appearance of heavy-tailed distributions in social sciences applications. Among these distributions are the laws of Pareto and Lotka and some new ones. The examples are illustrated through the construction of suitable toy models.

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