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

Arellano–Valle, Reinaldo B.; Contreras-Reyes, Javier E.; Stehlík, Milan

doi:10.3390/e19100528

Cited by 23 publications

(18 citation statements)

References 36 publications

(72 reference statements)

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“…Shannon entropy is a very important inferential measure to explain the variability or uncertainty of a random variable. The Shannon entropy for a random variable X with pdf f is given by (see [24,25]),…”

Section: Estimation Of the Parameters Of Asp With The Generalized Raymentioning

confidence: 99%

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Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Biçer

2019

Entropy

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In the modeling of successive arrival times with a monotone trend, the alpha-series process provides quite successful results. Both selecting the distribution of the first arrival time and making an optimal statistical inference play a crucial role in the modeling performance of the alpha-series process. In this study, when the distribution of the first arrival time is the generalized Rayleigh, the problem of statistical inference for the α , β , and λ parameters of the alpha-series process is considered. Further, in order to obtain optimal modeling performance from the mentioned alpha-series process, various estimators for the model parameters are obtained by employing different estimation methodologies such as maximum likelihood, modified maximum spacing, modified least-squares, modified moments, and modified L-moments. By a series of Monte Carlo simulations, the estimation efficiencies of the obtained estimators are evaluated through the different sample sizes. Finally, two real datasets are analyzed to illustrate the importance of modeling with the alpha-series process.

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Section: Estimation Of the Parameters Of Asp With The Generalized Raymentioning

confidence: 99%

“…The entropy measure of generalized Rayleigh distribution given by Equation (7) can be easily computed by using the (plug-in) estimators of the parameters obtained by the methods of ML, MMSP, MLS, MM, and MLM [24].…”

Section: Mls Estimationmentioning

confidence: 99%

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Biçer

2019

Entropy

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“…In this subsection, we investigate the Shannon and Rényi entropy, which are the two most popular entropies for Power Lindley distribution. The Shannon entropy (SE) of a random variable X with pdf f is defined as, see [21],…”

Section: Shannon and Rényi Entropy Of The Power Lindley Distributionmentioning

confidence: 99%

“…The elements of the Fisher information matrix I given by (21) are immediately written from elements of the Hessian matrix H (θ). However, an explicit form of the Fisher information matrix I cannot be derived.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Statistical Inference for Geometric Process with the Power Lindley Distribution

Biçer

2018

Entropy

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The geometric process (GP) is a simple and direct approach to modeling of the successive inter-arrival time data set with a monotonic trend. In addition, it is a quite important alternative to the non-homogeneous Poisson process. In the present paper, the parameter estimation problem for GP is considered, when the distribution of the first occurrence time is Power Lindley with parameters α and λ. To overcome the parameter estimation problem for GP, the maximum likelihood, modified moments, modified L-moments and modified least-squares estimators are obtained for parameters a, α and λ. The mean, bias and mean squared error (MSE) values associated with these estimators are evaluated for small, moderate and large sample sizes by using Monte Carlo simulations. Furthermore, two illustrative examples using real data sets are presented in the paper.

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“…The SRG distribution has as particular cases the Reflected-GZ and GZ distributions, when ε → 1 and ε → −1, respectively. The SRG distribution family can also represent a suitable competitor against the skew-normal (SN, [3]) and epsilon-skew-normal (ESN, [4]) distributions as a way to fit asymmetrical datasets. Indeed, refs.…”

Section: Introductionmentioning

confidence: 99%

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

Cited by 23 publications

References 36 publications

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Statistical Inference for Alpha-Series Process with the Generalized Rayleigh Distribution

Statistical Inference for Geometric Process with the Power Lindley Distribution

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

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