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Time Series of Counts under Censoring: A Bayesian Approach [PDF]
Entropy, 2023 Censored data are frequently found in diverse fields including environmental monitoring, medicine, economics and social sciences. Censoring occurs when observations are available only for a restricted range, e.g., due to a detection limit.
Isabel Silva +3 more
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Understanding Hierarchical Processes [PDF]
Entropy, 2022 Hierarchical stochastic processes, such as the hierarchical Dirichlet process, hold an important position as a modelling tool in statistical machine learning, and are even used in deep neural networks.
Wray Buntine
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Optimized Tail Bounds for Random Matrix Series [PDF]
EntropyRandom matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian ...
Xianjie Gao +2 more
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A New First-Order Integer-Valued Autoregressive Model with Bell Innovations [PDF]
Entropy, 2021 A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be ...
Jie Huang, Fukang Zhu
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The infimum values of two probability functions for the Gamma distribution [PDF]
Journal of Inequalities and ApplicationsLet α, β be positive real numbers and let X α , β $X_{\alpha ,\beta}$ be a Gamma random variable with shape parameter α and scale parameter β. We study infimum values of the function ( α , β ) ↦ P { X α , β ≤ κ E [ X α , β ] } $(\alpha ,\beta )\mapsto P\{
Ping Sun, Ze-Chun Hu, Wei Sun
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Regularity of Infinitely Divisible Processes
Annals of Probability, 1993 Some new tools are applied for the investigation of regularity properties of infinitely divisible random processes without Gaussian component, satisfying certain condition on its spectral measure. The majorizing measure is extended and applied to discuss the structure of bounded processes of this type.
Michel Talagrand
exaly +3 more sources
Infinite Divisibility of Information [PDF]
IEEE Transactions on Information Theory, 2021 We study an information analogue of infinitely divisible probability distributions, where the i.i.d. sum is replaced by the joint distribution of an i.i.d. sequence. A random variable $X$ is called informationally infinitely divisible if, for any $n\ge1$, there exists an i.i.d.
openaire +2 more sources
A New Bound in the Littlewood–Offord Problem
Mathematics, 2022 The paper deals with studying a connection of the Littlewood–Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.
Friedrich Götze, Andrei Yu. Zaitsev
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Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform
Mathematics, 2022 In this paper, we show that the local distribution class Lloc∩OSloc is not closed under infinitely divisible distribution roots, i.e., there is an infinitely divisible distribution which belongs to the class, while the corresponding Lévy distribution ...
Zhaolei Cui, Yuebao Wang, Hui Xu
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Some recent advances for limit theorems [PDF]
ESAIM: Proceedings and Surveys, 2020 We present some recent developments for limit theorems in probability theory, illustrating the variety of this field of activity. The recent results we discuss range from Stein’s method, as well as for infinitely divisible distributions as applications ...
Arras Benjamin +4 more
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