Article
Physics, Multidisciplinary
M. Derksen, B. Kleijn, R. de Vilder
Summary: This article studies the tails of closing auction return distributions for liquid European stocks and establishes a relationship between the tail exponents of limit order placement distributions and the resulting closing auction return distribution. The study finds that large closing price fluctuations are not typically driven by large market orders, but rather the tails become heavier when market orders are removed. The model explains this phenomenon by observing that limit orders are submitted to counter existing market order imbalances.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Physics, Fluids & Plasmas
Lana Descheemaeker, Jacopo Grilli, Sophie de Buyl
Summary: Microbial communities in nature are composed of many rare species and few abundant ones, with heavy-tailed abundance distributions. This study demonstrated how heavy-tailed distributions arise from interactions among many species in population-level models, as well as from specific parameter distributions in logistic models. Understanding both interactions and parameter distributions is crucial to explain the observed heavy tails in microbial communities.
Article
Computer Science, Interdisciplinary Applications
Denis Belomestny, Leonid Iosipoi
Summary: In this paper, a novel approach is proposed for utilizing MCMC algorithms in Fourier domain to sample from distributions with analytically known Fourier transforms, especially heavy-tailed distributions. By sampling from a density proportional to the absolute value of the characteristic function and applying Parseval's formula, an efficient algorithm for computing integrals with respect to the underlying density is obtained. The resulting Markov chain in Fourier domain is shown to be geometrically ergodic even in the case of heavy-tailed original distributions, as demonstrated through numerical examples.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics
Lev B. B. Klebanov, Yulia V. V. Kuvaeva-Gudoshnikova, Svetlozar T. T. Rachev
Summary: This paragraph provides two examples of heavy-tailed distributions in social sciences applications, including the laws of Pareto and Lotka and some new ones. The examples are illustrated through the construction of suitable toy models.
Article
Astronomy & Astrophysics
Sina Hooshangi, Mohammad Hossein Namjoo, Mahdiyar Noorbala
Summary: This paper investigates the limitations of perturbative treatment in predicting the abundance of primordial black holes (PBHs) and proposes a nonperturbative estimation method, called the SN formalism, for the tail of the probability distribution function (PDF). The results show that the SN formalism can provide more accurate predictions on the tail behavior, leading to a significant enhancement of PBH formation probability compared to perturbation theory.
Article
Statistics & Probability
Lvyun Zhang, Shouquan Chen
Summary: This paper proposes a new class of location-invariant semi-parametric estimators for a positive extreme value index gamma>0. The asymptotic distributional representation and asymptotic normality are derived and the optimal choice of the sample fraction by mean squared error is also discussed for some special cases. Finally, comparison studies are provided for some familiar models through Monte Carlo simulations.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Physics, Multidisciplinary
Kenric P. Nelson
Summary: A new statistical estimation method called Independent Approximates (IAs) is defined and proven to enable closed-form estimation of parameters for heavy-tailed distributions. IAs are formed by partitioning samples into different combinations and retaining the median of approximately equal groupings. The properties of IAs are studied and it is proven that heavy-tailed distributions have well-defined means, finite moments, and finite (n-1)th moments. The IA estimation methodology is then applied to the generalized Pareto and Student's t distributions, demonstrating good performance.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Statistics & Probability
David Deuber, Jinzhou Li, Sebastian Engelke, Marloes H. Maathuis
Summary: Causal inference for extreme events has potential applications in various fields. This study introduces a method for handling extreme quantiles and proposes a new causal Hill estimator. Simulation studies and application to a real dataset demonstrate the effectiveness of the method.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Engineering, Electrical & Electronic
Han Yu, Peng-Lang Shui, Kai Lu
Summary: This paper proposed an outlier-robust tri-percentile parameter estimator for K-distributions, which can effectively handle outliers in sea clutter data and shows strong robustness.
Article
Statistics & Probability
Johannes Heiny, Jianfeng Yao
Summary: This paper investigates the limiting distributions of eigenvalues of the sample correlation matrix when both the dimension and sample size grow to infinity. The moments of these limiting distributions are identified as a combination of the classical Marcenko-Pastur law and heavy tails. Furthermore, the family of limiting distributions has continuous extensions at the boundaries leading to different distributions.
ANNALS OF STATISTICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Jin Zhao, Zubair Ahmad, Eisa Mahmoudi, E. H. Hafez, Marwa M. Mohie El-Din
Summary: Statistical distributions, especially heavy-tailed distributions, are crucial for modeling actuarial and financial data. A new power transformation method is introduced to model heavy-tailed financial data, demonstrating its effectiveness through a submodel.
Article
Physics, Multidisciplinary
Haoyu Niu, Jiamin Wei, YangQuan Chen
Summary: The study aimed to improve the performance of SCN models by using heavy-tailed distributions for random initialization of weights and biases. Results showed that SCN models using heavy-tailed distributions performed better in regression and classification tasks, with some distributions allowing the models to achieve similar or even better results with fewer hidden nodes.
Article
Computer Science, Artificial Intelligence
Giannis Chantas, Spiros N. Nikolopoulos, Ioannis Kompatsiaris
Summary: The study introduces a novel probabilistic model based on image patch similarity for Single Image Super Resolution. Through comparison experiments and mathematical proofs, it shows that the algorithm outperforms Non-Local Means method in some cases but falls short in urban themed images compared to trained deep learning models. Additionally, qualitative evaluation using Perceptual Index metric favors this approach.
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2021)
Article
Computer Science, Information Systems
Muhammad Arif, Dost Muhammad Khan, Saima Khan Khosa, Muhammad Aamir, Adnan Aslam, Zubair Ahmad, Wei Gao
Summary: The article introduces a new class of heavy-tailed distributions for modeling data in financial sciences, specifically examining a new extended heavy-tailed Weibull distribution. The unknown parameters are estimated using maximum likelihood estimation method, with a simulation analysis performed to assess the performance. The proposed model is shown to be heavy-tailed empirically through actuarial measures, outperforming other competing models in a practical application to insurance loss data.
CMC-COMPUTERS MATERIALS & CONTINUA
(2021)
Article
Biology
Ying Jin, Dominik Rothenhaeusler
Summary: Parameters of finite populations with known attributes can be accurately estimated and have conditionally valid confidence intervals using a statistical inference framework. This allows for more relevant analysis of specific subpopulations and their effects, rather than generalizing from superpopulations. The proposed methods also extend to new populations with differing covariate distributions, providing conditionally valid confidence intervals.
Article
Statistics & Probability
Alain Desgagne
ANNALS OF STATISTICS
(2015)
Article
Statistics & Probability
A. Desgagne, P. Lafaye de Micheaux
JOURNAL OF APPLIED STATISTICS
(2018)
Article
Computer Science, Interdisciplinary Applications
Philippe Gagnon, Mylene Bedard, Alain Desgagne
MATHEMATICS AND COMPUTERS IN SIMULATION
(2019)
Article
Statistics & Probability
Alain Desgagne, Pierre Lafaye de Micheaux, Alexandre Leblanc
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2013)
Article
Clinical Neurology
Sophie Desjardins, Sylvie Lapierre, Carol Hudon, Alain Desgagne
Article
Statistics & Probability
Philippe Gagnon, Mylene Bedard, Alain Desgagne
Summary: Principal component regression uses PCs as regressors and is useful for prediction in high-dimensional covariate settings. A Bayesian approach is introduced for robust handling of outliers and efficient identification of significant components.
JOURNAL OF APPLIED STATISTICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Alain Desgagne
Summary: A new estimation method is proposed, offering high efficiency in the presence and absence of outliers simultaneously. This method broadens the error distribution to a mixture of normal and filtered log-Pareto distributions, and adjusts the EM algorithm for estimation. Monte Carlo simulations show that this method can be utilized for complete robust inference, including confidence intervals, hypothesis testing, and model selection.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2021)
Article
Computer Science, Interdisciplinary Applications
Alain Desgagne, Pierre Lafaye de Micheaux, Frederic Ouimet
Summary: This paper presents an empirical comparison of 40 goodness-of-fit tests for the univariate Laplace distribution using Monte Carlo simulations. The study includes sample sizes of 20, 50, 100, 200 and significance levels of 0.01, 0.05, 0.10. The results provide recommendations for the best tests and include a real-data example using weekly log-returns of Amazon stock.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2022)
Article
Statistics & Probability
Alain Desgagne, Pierre Lafaye de Micheaux, Frederic Ouimet
Summary: In this study, temperature data is modelled using the exponential power distribution. A family of goodness-of-fit tests is developed based on Pearson's skewness and kurtosis concepts, providing superior performance compared to other methods under various alternatives.
Article
Mathematics, Interdisciplinary Applications
Philippe Gagnon, Alain Desgagne, Mylene Bedard
Article
Mathematics, Interdisciplinary Applications
Alain Desgagne
Article
Public, Environmental & Occupational Health
S Perreault, A Dragomir, A Desgagné, L Blais, M Rossignol, J Blouin, Y Moride, LG Ste-Marie, JC Fernandès
PHARMACOEPIDEMIOLOGY AND DRUG SAFETY
(2005)
Article
Computer Science, Theory & Methods
A Desgagné, JF Angers
STATISTICS AND COMPUTING
(2005)
Article
Medicine, General & Internal
L Blais, A Desgagné, J LeLorier
ARCHIVES OF INTERNAL MEDICINE
(2000)