Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions

Arellano–Valle, Reinaldo B.; Contreras-Reyes, Javier E.; Genton, Marc G.

doi:10.1111/j.1467-9469.2011.00774.x

Cited by 83 publications

(84 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The SE of a localization-scale random variable X = µ + σZ does not depend on µ and is such that H(X) = log σ + H(Z) (see, e.g., [16]). The SE could serve to define a measure of disparity from normality, the so-called negentropy [17], which is zero for a Gaussian variable and positive for any distribution.…”

Section: Shannon Entropy and Related Measuresmentioning

confidence: 99%

“…Given that the calculus of negentropy presents a computational challenge, where the integral involves the pdf of Z [16,18], different approximations of negentropy are used, such as cumulants' expansion series [17,19]. Withers and Nadarajah [19] provided exact and explicit series expansions for the SE and negentropy of a standardized pdf f on R, in terms of cumulants.…”

Section: Shannon Entropy and Related Measuresmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Arellano–Valle

Contreras-Reyes

Stehlík

2017

Entropy

View full text Add to dashboard Cite

Abstract:The problem of measuring the disparity of a particular probability density function from a normal one has been addressed in several recent studies. The most used technique to deal with the problem has been exact expressions using information measures over particular distributions. In this paper, we consider a class of asymmetric distributions with a normal kernel, called Generalized Skew-Normal (GSN) distributions. We measure the degrees of disparity of these distributions from the normal distribution by using exact expressions for the GSN negentropy in terms of cumulants. Specifically, we focus on skew-normal and modified skew-normal distributions. Then, we establish the Kullback-Leibler divergences between each GSN distribution and the normal one in terms of their negentropies to develop hypothesis testing for normality. Finally, we apply this result to condition factor time series of anchovies off northern Chile.

show abstract

Section: Shannon Entropy and Related Measuresmentioning

confidence: 99%

Section: Shannon Entropy and Related Measuresmentioning

confidence: 99%

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Arellano–Valle

Contreras-Reyes

Stehlík

2017

Entropy

View full text Add to dashboard Cite

show abstract

“…In this section, we focus our attention principally on the skew-t model with ν (ν > 0) degrees of freedom (Branco and Dey, 2001;Azzalini and Capitanio, 2003;Arellano-Valle et al, 2012). This model follows by assuming in (3) that the mixing random factors v t are iid Gamma(ν/2, ν/2), i.e., with density given by…”

Section: The Skew-t Special Casementioning

confidence: 99%

Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Contreras-Reyes

Arellano–Valle²

2013

Fisheries Research

Self Cite

View full text Add to dashboard Cite

Our article presents a robust and flexible statistical modeling for the growth curve associated to the age-length relationship of Cardinalfish (Epigonus Crassicaudus). Specifically, we consider a non-linear regression model, in which the error distribution allows heteroscedasticity and belongs to the family of scale mixture of the skewnormal (SMSN) distributions, thus eliminating the need to transform the dependent variable into many data sets. The SMSN is a tractable and flexible class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work emphasis is given to the skew-t model. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by previous analysis about of Cardinalfish age, in which a maximum age of 15 years has been determined. Therefore, in this study we carry out the mentioned methodology over a data set that include a long-range of ages based on an otolith sample where the determined longevity is higher than 54 years.

show abstract

“…The entropy quantifies such uncertainty in bits which matches the scale of the exposure value. According to [26], based on Shannon's definition of entropy: …”

Section: B Desgining Exposure Certainty Functionmentioning

confidence: 99%

High dynamic range tone mapping based on Per-Pixel Exposure Mapping

Huang

Rampersad

Mann

2013

2013 IEEE International Symposium on Technology and Society (ISTAS): Social Implications of Wearable Computing and Augmediated

View full text Add to dashboard Cite

Abstract-The needs of a realtime vision aid require that it functions immediately, not merely for production of a picture or video record to be viewed later. Therefore the vision system must offer a high dynamic range (often hundreds of millions to one) that functions in real time. In compliment with the existing efficient and real-time HDR compositing algorithms, we propose a novel method for compressing High Dynamic Range (HDR) images by Per-Pixel Exposure Mapping (PPEM). Unlike any existing methods, PPEM only varies exposure to achieve tone mapping. It takes advantage of the camera response to enable exposure synthesis which we call Wyckoff set expansion. The method evaluates the synthetic exposures in a recursive pairwise process to generate a tone mapped HDR image. The results can be approximated using a look-up table, which can be used for real-time HDR applications.

show abstract

Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions

Cited by 83 publications

References 24 publications

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

High dynamic range tone mapping based on Per-Pixel Exposure Mapping

Contact Info

Product

Resources

About