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Open AccessEditor’s ChoiceArticle

Time Series of Counts under Censoring: A Bayesian Approach

by Isabel Silva, Maria Eduarda Silva, Isabel Pereira and Brendan McCabe

Entropy 2023, 25(4), 549; https://doi.org/10.3390/e25040549 - 23 Mar 2023

Cited by 3 | Viewed by 3004

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. Ignoring censoring produces biased estimates and unreliable statistical inference. The aim of this work is to contribute to the modelling of time series of counts under censoring using convolution closed infinitely divisible (CCID) models. The emphasis is on estimation and inference problems, using Bayesian approaches with Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA) algorithms. Full article

(This article belongs to the Special Issue Discrete-Valued Time Series)

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24 pages, 383 KB

Open AccessArticle

Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform

by Zhaolei Cui, Yuebao Wang and Hui Xu

Mathematics 2022, 10(21), 4128; https://doi.org/10.3390/math10214128 - 5 Nov 2022

Cited by 2 | Viewed by 1785

Abstract

In this paper, we show that the local distribution class

L_{l o c} \cap {OS}_{l o c}

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 [...] Read more.

In this paper, we show that the local distribution class

L_{l o c} \cap {OS}_{l o c}

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 does not. Conversely, we give a condition, under which, if an infinitely divisible distribution belongs to the class

L_{l o c} \cap {OS}_{l o c}

, then so does the Lévy distribution. Furthermore, we find some sufficient conditions that are more concise and intuitive. Using different methods, we also give a corresponding result for another local distribution class, which is larger than the above class. To prove the above results, we study the local closure under random convolution roots. In particular, we obtain a result on the local closure under the convolution root. In these studies, the Esscher transform of distribution plays a key role, which clarifies the relationship between these local distribution classes and related global distribution classes. Full article

(This article belongs to the Special Issue Distribution Theory and Application)

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