Entropy

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20 pages, 630 KiB

Open AccessArticle

Overcoming Dilution of Collision Probability in Satellite Conjunction Analysis via Confidence Distribution

by Hangbin Lee and Youngjo Lee

Entropy 2025, 27(4), 329; https://doi.org/10.3390/e27040329 - 21 Mar 2025

Viewed by 307

In satellite conjunction analysis, dilution of collision probability has been recognized as a significant deficiency of probabilistic inference. A recent study identified the false confidence problem as another limitation and suggested a possible causal link between the two, arguing that addressing false confidence [...] Read more.

In satellite conjunction analysis, dilution of collision probability has been recognized as a significant deficiency of probabilistic inference. A recent study identified the false confidence problem as another limitation and suggested a possible causal link between the two, arguing that addressing false confidence could be necessary to prevent dilution of collision probability. However, this paper clarifies the distinction between probability dilution and false confidence by investigating a confidence distribution (CD) with a point mass at zero. Although the point mass in CD has often been perceived as paradoxical, we demonstrate that it plays an essential role in satellite conjunction analysis by capturing the uncertainty in the data. Consequently, the CD resolves the probability dilution of probabilistic inference and the ambiguity in Neymanian confidence intervals, while addressing the false confidence for the hypothesis of interest in satellite conjunction analysis. Furthermore, the confidence derived from the CD offers a direct interpretation as a p-value for hypothesis testing related to collision risk. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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42 pages, 3013 KiB

Open AccessArticle

Optimal Power Procurement for Green Cellular Wireless Networks Under Uncertainty and Chance Constraints

by Nadhir Ben Rached, Shyam Mohan Subbiah Pillai and Raúl Tempone

Entropy 2025, 27(3), 308; https://doi.org/10.3390/e27030308 - 14 Mar 2025

Viewed by 471

Abstract

Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy-storage capacity, [...] Read more.

Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy-storage capacity, and hybrid energy systems comprising uncertain renewable energy sources. Despite the stochastic nature of wireless fading channels, the network operator must ensure a certain quality-of-service (QoS) constraint with high probability. This probabilistic constraint prevents using the dynamic programming principle to solve the stochastic optimal control problem. This work introduces a novel time-continuous Lagrangian relaxation approach tailored for real-time, near-optimal energy procurement in cellular networks, overcoming tractability problems associated with the probabilistic QoS constraint. The numerical solution procedure includes an efficient upwind finite-difference solver for the Hamilton–Jacobi–Bellman equation corresponding to the relaxed problem, and an effective combination of the limited memory bundle method (LMBM) for handling nonsmooth optimization and the stochastic subgradient method (SSM) to navigate the stochasticity of the dual problem. Numerical results, based on the German power system and daily cellular traffic data, demonstrate the computational efficiency of the proposed numerical approach, providing a near-optimal policy in a practical timeframe. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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19 pages, 4184 KiB

Open AccessArticle

An Online Evaluation Method for Random Number Entropy Sources Based on Time-Frequency Feature Fusion

by Qian Sun, Kainan Ma, Yiheng Zhou, Zhaoyuxuan Wang, Chaoxing You and Ming Liu

Entropy 2025, 27(2), 136; https://doi.org/10.3390/e27020136 - 27 Jan 2025

Viewed by 671

Abstract

Traditional entropy source evaluation methods rely on statistical analysis and are hard to deploy on-chip or online. However, online detection of entropy source quality is necessary in some applications with high encryption levels. To address these issues, our experimental results demonstrate a significant [...] Read more.

Traditional entropy source evaluation methods rely on statistical analysis and are hard to deploy on-chip or online. However, online detection of entropy source quality is necessary in some applications with high encryption levels. To address these issues, our experimental results demonstrate a significant negative correlation between minimum entropy values and prediction accuracy, with a Pearson correlation coefficient of −0.925 (p-value = 1.07 × 10⁻⁷). This finding offers a novel approach for assessing entropy source quality, achieving an accurate rate in predicting the next bit of a random sequence using neural networks. To further improve prediction capabilities, we also propose a novel deep learning architecture, Fast Fourier Transform-Attention Mechanism-Long Short-Term Memory Network (FFT-ATT-LSTM), that integrates a simplified soft attention mechanism with Fast Fourier Transform (FFT), enabling effective fusion of time-domain and frequency-domain features. The FFT-ATT-LSTM improves prediction accuracy by 4.46% and 8% over baseline networks when predicting random numbers. Additionally, FFT-ATT-LSTM maintains a compact parameter size of 33.90 KB, significantly smaller than Temporal Convolutional Networks (TCN) at 41.51 KB and Transformers at 61.51 KB, while retaining comparable prediction performance. This optimal balance between accuracy and resource efficiency makes FFT-ATT-LSTM suitable for online deployment, demonstrating considerable application potential. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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22 pages, 1347 KiB

Open AccessArticle

Semi-Empirical Approach to Evaluating Model Fit for Sea Clutter Returns: Focusing on Future Measurements in the Adriatic Sea

by Bojan Vondra

Entropy 2024, 26(12), 1069; https://doi.org/10.3390/e26121069 - 9 Dec 2024

Cited by 1 | Viewed by 708

Abstract

A method for evaluating Kullback–Leibler (KL) divergence and Squared Hellinger (SH) distance between empirical data and a model distribution is proposed. This method exclusively utilises the empirical Cumulative Distribution Function (CDF) of the data and the CDF of the model, avoiding data processing [...] Read more.

A method for evaluating Kullback–Leibler (KL) divergence and Squared Hellinger (SH) distance between empirical data and a model distribution is proposed. This method exclusively utilises the empirical Cumulative Distribution Function (CDF) of the data and the CDF of the model, avoiding data processing such as histogram binning. The proposed method converges almost surely, with the proof based on the use of exponentially distributed waiting times. An example demonstrates convergence of the KL divergence and SH distance to their true values when utilising the Generalised Pareto (GP) distribution as empirical data and the K distribution as the model. Another example illustrates the goodness of fit of these (GP and K-distribution) models to real sea clutter data from the widely used Intelligent PIxel processing X-band (IPIX) measurements. The proposed method can be applied to assess the goodness of fit of various models (not limited to GP or K distribution) to clutter measurement data such as those from the Adriatic Sea. Distinctive features of this small and immature sea, like the presence of over 1300 islands that affect local wind and wave patterns, are likely to result in an amplitude distribution of sea clutter returns that differs from predictions of models designed for oceans or open seas. However, to the author’s knowledge, no data on this specific topic are currently available in the open literature, and such measurements have yet to be conducted. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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20 pages, 430 KiB

Open AccessArticle

On the Stress–Strength Reliability of Transmuted GEV Random Variables with Applications to Financial Assets Selection

by Melquisadec Oliveira, Felipe S. Quintino, Dióscoros Aguiar, Pushpa N. Rathie, Helton Saulo, Tiago A. da Fonseca and Luan Carlos de Sena Monteiro Ozelim

Entropy 2024, 26(6), 441; https://doi.org/10.3390/e26060441 - 23 May 2024

Viewed by 1010

Abstract

In reliability contexts, probabilities of the type

R = P (X < Y)

, where X and Y are random variables, have shown to be useful tools to compare the performance of these stochastic entities. By considering that both X and [...] Read more.

In reliability contexts, probabilities of the type

R = P (X < Y)

, where X and Y are random variables, have shown to be useful tools to compare the performance of these stochastic entities. By considering that both X and Y follow a transmuted generalized extreme-value (TGEV) distribution, new analytical relationships were derived for R in terms of special functions. The results hereby obtained are more flexible when compared to similar results found in the literature. To highlight the applicability and correctness of our results, we conducted a Monte-Carlo simulation study and investigated the use of the reliability measure

P (X < Y)

to select among financial assets whose returns were characterized by the random variables X and Y. Our results highlight that R is an interesting alternative to modern portfolio theory, which usually relies on the contrast of involved random variables by a simple comparison of their means and standard deviations. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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13 pages, 539 KiB

Open AccessFeature PaperArticle

Estimation of a Simple Structure in a Multidimensional IRT Model Using Structure Regularization

by Ryosuke Shimmura and Joe Suzuki

Entropy 2024, 26(1), 44; https://doi.org/10.3390/e26010044 - 31 Dec 2023

Viewed by 1533

Abstract

We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items [...] Read more.

We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items based on their corresponding latent traits. The basic idea of our approach is to use the prenet (product-based elastic net) penalty, as proposed in factor analysis. For optimization, we show that combining stochastic EM algorithms, proximal gradient methods, and coordinate descent methods efficiently yields solutions. Furthermore, our numerical experiments demonstrate its effectiveness, especially in cases where the number of test subjects is small, compared to methods using the existing

L_{1}

penalty. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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14 pages, 770 KiB

Open AccessArticle

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

by Cira G. Otiniano, Eduarda B. Silva, Raul Y. Matsushita and Alan Silva

Entropy 2023, 25(12), 1598; https://doi.org/10.3390/e25121598 - 29 Nov 2023

Viewed by 1334

Abstract

This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in [...] Read more.

This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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13 pages, 1184 KiB

Open AccessArticle

Gaussian and Lerch Models for Unimodal Time Series Forcasting

by Azzouz Dermoune, Daoud Ounaissi and Yousri Slaoui

Entropy 2023, 25(10), 1474; https://doi.org/10.3390/e25101474 - 22 Oct 2023

Viewed by 1639

Abstract

We consider unimodal time series forecasting. We propose Gaussian and Lerch models for this forecasting problem. The Gaussian model depends on three parameters and the Lerch model depends on four parameters. We estimate the unknown parameters by minimizing the sum of the absolute [...] Read more.

We consider unimodal time series forecasting. We propose Gaussian and Lerch models for this forecasting problem. The Gaussian model depends on three parameters and the Lerch model depends on four parameters. We estimate the unknown parameters by minimizing the sum of the absolute values of the residuals. We solve these minimizations with and without a weighted median and we compare both approaches. As a numerical application, we consider the daily infections of COVID-19 in China using the Gaussian and Lerch models. We derive a confident interval for the daily infections from each local minima. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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33 pages, 804 KiB

Open AccessArticle

Kolmogorov Entropy for Convergence Rate in Incomplete Functional Time Series: Application to Percentile and Cumulative Estimation in High Dimensional Data

by Ouahiba Litimein, Fatimah Alshahrani, Salim Bouzebda, Ali Laksaci and Boubaker Mechab

Entropy 2023, 25(7), 1108; https://doi.org/10.3390/e25071108 - 24 Jul 2023

Cited by 2 | Viewed by 1637

Abstract

The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is [...] Read more.

The convergence rate for free-distribution functional data analyses is challenging. It requires some advanced pure mathematics functional analysis tools. This paper aims to bring several contributions to the existing functional data analysis literature. First, we prove in this work that Kolmogorov entropy is a fundamental tool in characterizing the convergence rate of the local linear estimation. Precisely, we use this tool to derive the uniform convergence rate of the local linear estimation of the conditional cumulative distribution function and the local linear estimation conditional quantile function. Second, a central limit theorem for the proposed estimators is established. These results are proved under general assumptions, allowing for the incomplete functional time series case to be covered. Specifically, we model the correlation using the ergodic assumption and assume that the response variable is collected with missing at random. Finally, we conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimators. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

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