Shannon entropy and Kullback–Leibler divergence in multivariate log fundamental skew‐normal and related distributions

Queiroz, Marina M. de; Silva, Roger W. C.; Loschi, Rosangela H.

doi:10.1002/cjs.11285

Cited by 4 publications

(5 citation statements)

References 25 publications

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“…Moreover, several recent investigations confirmed the usefulness of entropic quantifiers in the study of asymmetric distributions [3,7,8] and their applications to topics such as thermal wake [9], marine fish biology [3,8], sea surface temperature (SST), relative humidity measured in the Atlantic Ocean [10], and more. We build on the study of [3], which developed hypothesis testing for normality, i.e., if the shape parameter is close to zero.…”

Section: Introductionmentioning

confidence: 88%

“…From (10), given that H(X ±ε ) only depends on shape parameter η, we obtain H(X ±ε ) = H(X), and H(Y) only depends on η and ε parameters. Therefore,…”

Section: Shannon Entropymentioning

confidence: 95%

“…This work arose from a motivation to tackle the problem of determining the adequate pdf of SST [9,10]. Indeed, probabilistic modelling of SST is key for accurate predictions [9].…”

Section: Introductionmentioning

confidence: 99%

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Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records

2019

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The Skew-Reflected-Gompertz (SRG) distribution, introduced by Hosseinzadeh et al. (J. Comput. Appl. Math. (2019) 349, 132–141), produces two-piece asymmetric behavior of the Gompertz (GZ) distribution, which extends the positive to a whole dominion by an extra parameter. The SRG distribution also permits a better fit than its well-known classical competitors, namely the skew-normal and epsilon-skew-normal distributions, for data with a high presence of skewness. In this paper, we study information quantifiers such as Shannon and Rényi entropies, and Kullback–Leibler divergence in terms of exact expressions of GZ information measures. We find the asymptotic test useful to compare two SRG-distributed samples. Finally, as a real-world data example, we apply these results to South Pacific sea surface temperature records.

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Section: Introductionmentioning

confidence: 88%

“…From (10), given that H(X ±ε ) only depends on shape parameter η, we obtain H(X ±ε ) = H(X), and H(Y) only depends on η and ε parameters. Therefore,…”

Section: Shannon Entropymentioning

confidence: 95%

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Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records

2019

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“…Thanks to its characteristics, Shannon entropy is a popular method, not only for fault detection but also for other applications, such as for the analysis of biological signals [12], computational applications [13], and environmental data [14].…”

Section: Shannon Entropymentioning

confidence: 99%

Entropy-Based Methods for Motor Fault Detection: A Review

Aguayo-Tapia,

Avalos-Almazan,

Rangel-Magdaleno

2024

Entropy

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In the signal analysis context, the entropy concept can characterize signal properties for detecting anomalies or non-representative behaviors in fiscal systems. In motor fault detection theory, entropy can measure disorder or uncertainty, aiding in detecting and classifying faults or abnormal operation conditions. This is especially relevant in industrial processes, where early motor fault detection can prevent progressive damage, operational interruptions, or potentially dangerous situations. The study of motor fault detection based on entropy theory holds significant academic relevance too, effectively bridging theoretical frameworks with industrial exigencies. As industrial sectors progress, applying entropy-based methodologies becomes indispensable for ensuring machinery integrity based on control and monitoring systems. This academic endeavor enhances the understanding of signal processing methodologies and accelerates progress in artificial intelligence and other modern knowledge areas. A wide variety of entropy-based methods have been employed for motor fault detection. This process involves assessing the complexity of measured signals from electrical motors, such as vibrations or stator currents, to form feature vectors. These vectors are then fed into artificial-intelligence-based classifiers to distinguish between healthy and faulty motor signals. This paper discusses some recent references to entropy methods and a summary of the most relevant results reported for fault detection over the last 10 years.

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“…. , M, are assumed to be equal its mean value (ϕ i ) = 0, µ i s (t) ≡ µ s (t), 1 ≤ s ≤ 4, moreover, taking into account stochastic representations of log-skew elliptical random vectors [39], the expressions for univariate and multivariate Shannon entropies (measured in nats) take the following forms [40]: σ 22 ,α 3 ,β 3 ,γ 3 ,σ 33 ,α 4 ,β 4 ,γ 4 ,σ 44 ,σ 12 ,σ 13 ,σ 14 ,σ 23 ,σ 24 ,σ 34 As we can see from Equation 45, the mutual information, I, is calculated directly by summing the individual entropies and subtracting the joint entropy. Mutual information, I, between two random variables, X s and X u , compares the uncertainty of measuring variables jointly with the uncertainty of measuring the two variables independently, identifies nonlinear dependence between two variables [41][42][43], and is non-negative and symmetrical.…”

Section: Information Measuresmentioning

confidence: 99%

Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

Rupšys

2019

Mathematics

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This study focuses on the stochastic differential calculus of Itô, as an effective tool for the analysis of noise in forest growth and yield modeling. Idea of modeling state (tree size) variable in terms of univariate stochastic differential equation is exposed to a multivariate stochastic differential equation. The new developed multivariate probability density function and its marginal univariate, bivariate and trivariate distributions, and conditional univariate, bivariate and trivariate probability density functions can be applied for the modeling of tree size variables and various stand attributes such as the mean diameter, height, crown base height, crown width, volume, basal area, slenderness ratio, increments, and much more. This study introduces generalized multivariate interaction information measures based on the differential entropy to capture multivariate dependencies between state variables. The present study experimentally confirms the effectiveness of using multivariate interaction information measures to reconstruct multivariate relationships of state variables using measurements obtained from a real-world data set.

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Shannon entropy and Kullback–Leibler divergence in multivariate log fundamental skew‐normal and related distributions

Cited by 4 publications

References 25 publications

Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records

Skew-Reflected-Gompertz Information Quantifiers with Application to Sea Surface Temperature Records

Entropy-Based Methods for Motor Fault Detection: A Review

Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

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