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Journal articles on the topic 'R`enyi's entropy'

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Published: 3 June 2025
Last updated: 19 July 2025

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1

Bebiano, Natalia, Joao Da Providencia, and J. P. Da Providencia. "R\'enyi's quantum thermodynamical inequalities." Electronic Journal of Linear Algebra 33 (May 16, 2018): 63–73. http://dx.doi.org/10.13001/1081-3810.3665.

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A theory of thermodynamics has been recently formulated and derived on the basis of R\'enyi entropy and its relative versions. In this framework, the concepts of partition function, internal energy and free energy are defined, and fundamental quantum thermodynamical inequalities are deduced. In the context of R\'enyi's thermodynamics, the variational Helmholtz principle is stated and the condition of equilibrium is analyzed. The %obtained results reduce to the von Neumann ones when the R\'enyi entropic parameter $\alpha$ approaches 1. The main goal of the article is to give simple and self-con
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2

Rastegin, Alexey E. "Renyi and Tsallis formulations of noise-disturbance trade-off relations." Quantum Information and Computation 16, no. 3&4 (2016): 313–31. http://dx.doi.org/10.26421/qic16.3-4-7.

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We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R´enyi and Tsallis entropies. Related information-theoretic measures of noise and disturbance are introduced. These definitions are based on the concept of conditional entropy. To motivate introduced measures, some important properties of the conditional R´enyi and Tsallis entropies are discussed. There exist several formulations of entropic uncertainty relations for a pair of observables. Trade-off relations
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3

Jebril, Iqbal H., Raed Hatamleh, Iqbal Batiha, and Nadia Allouch. "Application of Ujlayan-Dixit Fractional Chi-Square Probability Distribution." Statistics, Optimization & Information Computing 14, no. 1 (2025): 373–86. https://doi.org/10.19139/soic-2310-5070-2334.

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In this study, we take into account the Ujlayan-Dixit (UD) fractional derivative in order to introduce the fractional probability density function for the Chi-Square distribution (CSD), and to establish certain new applications for this distribution through the use of fractional concepts in probability theory, such as cumulative distribution, survival, and hazard functions. Furthermore, other ideas and applications for continuous random variables are developed using the UD fractional analogs of statistical measures, which are expectation, rth-moments, rth-central moments, variance, and standar
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4

Lak, Fazlollah, Morad Alizadeh, and Hamid Karamikabir. "The Topp-Leone odd log-logistic Gumbel Distribution: Properties and Applications." Statistics, Optimization & Information Computing 9, no. 2 (2020): 288–310. http://dx.doi.org/10.19139/soic-2310-5070-903.

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In this article, the Topp-Leone odd log-logistic Gumbel (TLOLL-Gumbel) family of distribution have beenstudied. This family, contains the very flexible skewed density function. We study many aspects of the new model like hazard rate function, asymptotics, useful expansions, moments, generating Function, R´enyi entropy and order statistics. We discuss maximum likelihood estimation of the model parameters. Further, we study flexibility of the proposed family are illustrated of two real data sets.
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Makubate, Boikanyo, Broderick Oluyede, and Morongwa Gabanakgosi. "A New Lindley-Burr XII Distribution: Model, Properties and Applications." International Journal of Statistics and Probability 10, no. 4 (2021): 33. http://dx.doi.org/10.5539/ijsp.v10n4p33.

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A new distribution called the Lindley-Burr XII (LBXII) distribution is proposed and studied. Some structural properties of the new distribution including moments, conditional moments, distribution of the order statistics and R´enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and applications to real data sets in order to illustrate the usefulness of the new distribution are given.
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6

Mashabe, Baitshephi, Broderick O. Oluyede, Adeniyi F. Fagbamigbe, Boikanyo Makubate, and Syamala Krishnannair. "A New Class of Generalized Weibull-G Family of Distributions: Theory, Properties and Applications." International Journal of Statistics and Probability 8, no. 1 (2018): 73. http://dx.doi.org/10.5539/ijsp.v8n1p73.

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We propose a generalized class of distributions called the Webull-G Power Series (WGPS) family of distributions and its sub-model Weibull-G logarithmic (WGL) distributions. Structural properties of the WGPS family of distributions and its sub-model WGL distribution including hazard function, moments, conditional moments, order statistics, R´enyi entropy and maximum likelihood estimates are derived. A simulation study to examine the bias, mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the
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7

Chipepa, Fastel, Broderick O. Oluyede, and Boikanyo Makubate. "A New Generalized Family of Odd Lindley-G Distributions With Application." International Journal of Statistics and Probability 8, no. 6 (2019): 1. http://dx.doi.org/10.5539/ijsp.v8n6p1.

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A new family of distributions, namely the Kumaraswamy Odd Lindley-G distribution is developed. The new density function can be expressed as a linear combination of exponentiated-G densities. Statistical properties of the new family including hazard rate and quantile functions, moments and incomplete moments, Bonferroni and Lorenz curves, distribution of order statistics and R´enyi entropy are derived. Some special cases are presented. We conduct some Monte Carlo simulations to examine the consistency of the maximum likelihood estimates. We provide an application of KOL-LLo distributi
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8

Popescu, Theodor D. "Energy Distribution Evaluation Using Renyi Entropy Measures With Application in EEG Data Analysis." WSEAS TRANSACTIONS ON SIGNAL PROCESSING 17 (September 29, 2021): 99–107. http://dx.doi.org/10.37394/232014.2021.17.14.

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The ”corrected” EEG recordings, after artifact removing, may be the subject of further investigations, for example segmentation and energy distribution, resulting new informa- tion to be used for feature extraction, of great help for medical diagnosis. The paper presents a generally method for energy distribution evalua- tion using measures of R´enyi entropy. The pre- sented approach ensures the possibility of quan- titative analysis of the information contained in time-frequency distribution of EEG signals. The proposed procedure is applied with good results in the analysis of a sample lowpas
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9

De Andrade, Thiago A. N., Luz Milena Zea Fernandez, Frank Gomes-Silva, and Gauss M. Cordeiro. "The Gamma Generalized Pareto Distribution with Applications in Survival Analysis." International Journal of Statistics and Probability 6, no. 3 (2017): 141. http://dx.doi.org/10.5539/ijsp.v6n3p141.

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We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Car
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10

Oluyede, Broderick. "The Gamma-Weibull-G Family of Distributions with Applications." Austrian Journal of Statistics 47, no. 1 (2018): 45–76. http://dx.doi.org/10.17713/ajs.v47i1.155.

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Weibull distribution and its extended families has been widely studied in lifetime applications. Based on the Weibull-G family of distributions and the exponentiated Weibull distribution, we study in detail this new class of distributions, namely, Gamma-WeibullG family of distributions (GWG). Some special models in the new class are discussed. Statistical properties of the family of distributions, such as expansion of density function, hazard and reverse hazard functions, quantile function, moments, incomplete moments, generating functions, mean deviations, Bonferroni and Lorenz curves and ord
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11

Oluyede, Broderick, Morongwa Gabanakgosi, and Gayan Warahena-Liyanage. "The Marshall-Olkin-Topp-Leone-Gompertz-G Family of Distributions with Applications." Statistics, Optimization & Information Computing 12, no. 4 (2024): 882–906. http://dx.doi.org/10.19139/soic-2310-5070-1509.

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A new family of distributions called the Marshall-Olkin-Topp-Leone-Gompertz-G (MO-TL-Gom-G) distribution is developed and studied in detail. Some mathematical and statistical properties of the new family of distributions are explored. Statistical properties of the new family of distributions considered are the quantile function, moments and generating function, probability weighted moments, distribution of the order statistics and R\'enyi entropy. The maximum likelihood technique is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of t
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12

O. Oluyede, Broderick, Huybrechts F. Bindele, Boikanyo Makubate, and Shujiao Huang. "A New Generalized Log-logistic and Modified Weibull Distribution with Applications." International Journal of Statistics and Probability 7, no. 3 (2018): 72. http://dx.doi.org/10.5539/ijsp.v7n3p72.

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A new generalized distribution called the {\em log-logistic modified Weibull} (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Loren
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13

Carrasco, Jalmar M. F., and Gauss M. Cordeiro. "An Extension of the Kumaraswamy Distribution." International Journal of Statistics and Probability 6, no. 3 (2017): 61. http://dx.doi.org/10.5539/ijsp.v6n3p61.

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We propose and study a new five-parameter continuous distribution in the unit interval through a specific probability integral transform. The new distribution, under some parameter constraints, is an identified parametric model that includes as special cases six important models such as the Kumaraswamy and beta distributions. We obtain ordinary and incomplete moments, quantile and generating functions, mean deviations, R\'enyi entropy and moments of order statistics. The estimation of the model parameters is performed by maximum likelihood, and hypothesis tests are discussed. Additionally, thr
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14

Adeyinka, Femi Samuel. "On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications." European Journal of Statistics 2 (November 22, 2021): 2. http://dx.doi.org/10.28924/ada/stat.2.2.

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This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed. The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the mo
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15

Makubate, Boikanyo, Broderick O. Oluyede, Gofaone Motobetso, Shujiao Huang, and Adeniyi F. Fagbamigbe. "The Beta Weibull-G Family of Distributions: Model, Properties and Application." International Journal of Statistics and Probability 7, no. 2 (2018): 12. http://dx.doi.org/10.5539/ijsp.v7n2p12.

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A new family of generalized distributions called the beta Weibull-G (BWG) distribution is proposed and developed. This new class of distributions has several new and well known distributions including exponentiated-G, Weibull-G, Rayleigh-G, exponential-G, beta exponential-G, beta Rayleigh-G, beta Rayleigh exponential, beta-exponential-exponential, Weibull-log-logistic distributions, as well as several other distributions such as beta Weibull-Uniform, beta Rayleigh-Uniform, beta exponential-Uniform, beta Weibull-log logistic and beta Weibull-exponential distributions as special cases. Series ex
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16

Makubate, Boikanyo, Broderick O. Oluyede, Neo Dingalo, and Adeniyi Francis Fagbamigbe. "The Beta Log-Logistic Weibull Distribution: Model, Properties and Application." International Journal of Statistics and Probability 7, no. 6 (2018): 49. http://dx.doi.org/10.5539/ijsp.v7n6p49.

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We propose and develop the properties of a new generalized distribution called the beta log-logistic Weibull (BLLoGW) distribution. This model contain several new distributions such as beta log-logistic Rayleigh, beta log-logistic exponential, exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential,  log-logistic Weibull, log-logistic Rayleigh and log-logistic distributions as special cases. Structural properties of this generalized distribution including series expansion of the probability density function and cumulative distrib
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17

Musekwa, Regent Retrospect, Boikanyo Makubate, and Violet Nyamajiwa. "The Odd Generalized Rayleigh Reciprocal Weibull Family of Distributions with Applications." Statistics, Optimization & Information Computing 13, no. 3 (2025): 1320–38. https://doi.org/10.19139/soic-2310-5070-2194.

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We introduced a novel family of models in this paper, which we named the odd-generalized Rayleigh reciprocalWeibull-G (OGR-RW-G) family. This family is noteworthy because it applies the T-X model construction technique to the generalized Rayleigh reciprocal Weibull model, addressing the inflexibility limits associated with traditional models and allowing one to use any baseline distribution. We examine some valuable statistical inferences from the OGR-RW-G, including its probability density function (pdf) represented in a linear fashion, its order statistics’ pdf, moments, residual life functi
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18

Alsaggaf, Ibtesam. "Analyzing Cancer Survival Times Using the Exponentiated Fréchet-Gompertz Distribution." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3856–98. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5471.

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Understanding the survival of cancer patients is essential for determining optimal treatment strategies. This research introduces a robust distribution for analyzing survival data known as the Exponential Fr ́echet-Gompertz distribution (EFG). The EFG combines the unique characteristics of the Exponential Fr ́echet and Gompertz distributions, enhancing its efficiency and providing greater flexibility in representing complex datasets. The study specifically investigates the EFG distribution’s effectiveness in modeling cancer patients’ survival times. A comprehensive analysis of the distribution
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19

Rajkumar, Verma and Bhu dev Sharma. "Entropic Measures of a Probability Sample Space and Exponential Type (alpha, beta) entropy." International Journal of Electronics and Communication Engineering 7.0, no. 11 (2013). https://doi.org/10.5281/zenodo.2659026.

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Entropy is a key measure in studies related to information theory and its many applications. Campbell for the first time recognized that the exponential of the Shannon's entropy is just the size of the sample space, when distribution is uniform. Here is the idea to study exponentials of Shannon's and those other entropy generalizations that involve logarithmic function for a probability distribution in general. In this paper, we introduce a measure of sample space, called 'entropic measure of a sample space', with respect to the underlying distribution. It is shown in both discrete and continu
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20

Rajkumar, Verma, та Dev Sharma Bhu. "Entropic Measures of a Probability Sample Space and Exponential Type (α, β) Entropy". 6 січня 2014. https://doi.org/10.5281/zenodo.1090556.

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Entropy is a key measure in studies related to information theory and its many applications. Campbell for the first time recognized that the exponential of the Shannon’s entropy is just the size of the sample space, when distribution is uniform. Here is the idea to study exponentials of Shannon’s and those other entropy generalizations that involve logarithmic function for a probability distribution in general. In this paper, we introduce a measure of sample space, called ‘entropic measure of a sample space’, with respect to the underlying distribution. It is shown in b
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21

Siddik, Sk, and Golam Ali Sekh. "Information theoretic measures on quantum droplets in ultracold atomic systems." Physica Scripta, September 26, 2024. http://dx.doi.org/10.1088/1402-4896/ad8046.

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Abstract We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang correction gives a family of quantum droplets with different chemical potentials. At a larger value of chemical potential, quantum droplet with sharp-top probability density distribution starts to form while it becomes flat top for a smaller value of chemical potential. We show that entropic measures can distinguish the shape change of the probabilit
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22

Sriling, Peerawat, Ratchaphat Nakarachinda, and Pitayuth Wongjun. "Thermodynamics of black string from R\'enyi entropy in de Rham-Gabadadze-Tolley massive gravity theory." Classical and Quantum Gravity, May 31, 2022. http://dx.doi.org/10.1088/1361-6382/ac750b.

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Abstract The de Rham-Gabadadze-Tolley (dRGT) black string solution is a cylindrically symmetric and static solution of the Einstein field equation with graviton mass term. For the asymptotically de Sitter (dS) solution, it is possible to obtain the black string with two event horizons corresponding to two thermodynamic systems. The R\'enyi entropy is one of the entropic forms which is suitable to deal with nonextensive properties of the black string. In this work, we investigated the possibility to obtain a stable black string by using the R\'enyi entropy in both separated and effective approa
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23

Liu, Yutong, Hua Nan, Lin Zhang, Yan Jin, and Yi-Cheng Hong. "Entropy-Based Geometric Measures of Correlations for Bell Diagonal States via Measurement." Physica Scripta, October 21, 2024. http://dx.doi.org/10.1088/1402-4896/ad897d.

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Abstract The classification and quantification of quantum correlations are the important issues in quantum information theory. Quantum relative entropy and R´enyi relative entropy are both non-negative, and can therefore be regarded as generalized distances between quantum states. We first introduced the method proposed by Brodutch and Modi for constructing measurements of classical and quantum correlations. Subsequently, we use this method to construct measurement-induced geometric classical and quantum correlations based on quantum relative entropy and R´enyi relative entropy (a = 1/2 ). For
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24

Its, A. R., and V. E. Korepin. "The Fisher-Hartwig Formula and Entanglement Entropy." December 1, 2009. https://doi.org/10.1007/s10955-009-9835-9.

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Toeplitz matrices have applications to different problems of statis- tical mechanics. Recently it was used for calculation of entanglement entropy in exactly solvable models including spin chains. We use Fisher-Hartwig for- mula to calculate entanglement entropy [as well as R´enyi entropy] of large block of spins in the ground state of XY spin chain. In the end of the paper we announce our recent results [with F. Franchini and L. A. Takhtajan] on spectrum of density matrix of the block of spins.
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25

Dolbeault, Jean, Maria J. Esteban, and Michael Loss. "Symmetry and symmetry breaking: rigidity and flows in elliptic PDEs." January 1, 2018. https://doi.org/10.5281/zenodo.3660432.

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This paper collects results concerning global rates and large time asymptotics of a fractional fast diffusion on the Euclidean space, which is deeply related with a family of fractional Gagliardo-Nirenberg-Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo-Nirenberg-Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carr ́e du champ and R ́enyi entropy powers methods are investigated and rai
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26

Keseman, Theo, Hans Muneesamy, and Yasaman Yazdi. "Insights on Entanglement Entropy in 1+1 Dimensional Causal Sets." Classical and Quantum Gravity, March 22, 2022. http://dx.doi.org/10.1088/1361-6382/ac5fc0.

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Abstract Entanglement entropy in causal sets offers a fundamentally covariant characterisation of quantum field degrees of freedom. A known result in this context is that the degrees of freedom consist of a number of contributions that have continuum-like analogues, in addition to a number of contributions that do not. The latter exhibit features below the discreteness scale and are excluded from the entanglement entropy using a ``truncation scheme''. This truncation is necessary to recover the standard spatial area law of entanglement entropy. In this paper we build on previous work on the en
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27

Aydın, Demet. "THE NEW WEIGHTED INVERSE RAYLEIGH DISTRIBUTION AND ITS APPLICATION." Facta Universitatis, Series: Mathematics and Informatics, October 4, 2019, 511. http://dx.doi.org/10.22190/fumi1903511a.

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In this study, a new weighted version of the inverse Rayleigh distribution based on two different weight functions is introduced. Some statistical and reliability properties of the introduced distribution including the moments, moment generating function, entropy measures (i.e., Shannon and R´enyi) and survival and hazard rate functions are derived. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms. So, a numerical method has been required to compute maximum likelihood estimates. Finally, the daily mean wind speed data set has been analysed to sho
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28

Falgore, Jamilu Yunusa. "The Zubair-Inverse Lomax Distribution with Applications." Asian Journal of Probability and Statistics, August 11, 2020, 1–14. http://dx.doi.org/10.9734/ajpas/2020/v8i330206.

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In this article, an extension of Inverse Lomax (IL) distribution with the Zubair-G family is considered . Various statistical properties of the new model where derived, including moment generating function, R´enyi entropy, and order statistics. A Monte Carlo simulation study was presented to evaluate the performance of the maximum likelihood estimators. The new model can be skew to the right, constant, and decreasing functions depending on the parameter values.We discussed the estimation of the model parameters by maximum likelihood method. The application of the new model to the data sets ind
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29

Gabanakgosi, Morongwa, and Broderick Oluyede. "The Topp-Leone-Gompertz-G Power Series Class of Distributions with Applications." Pakistan Journal of Statistics and Operation Research, June 5, 2024, 171–95. https://doi.org/10.18187/pjsor.v20i2.4032.

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A new generalized class of distributions called the Topp-Leone-Gompertz-G Power Series (TL-Gom-GPS) distribution is presented. Some mathematical and statistical properties of the new class of distributions are explored. For this new class of distributions, we derived the quantile function, moments and generating function, probability weighted moments, distribution of the order statistics and R\'enyi entropy. The maximum likelihood technique is used for estimating model parameters and Monte Carlo simulation is conducted to show the performance of the proposed model. Finally, the usefulness and
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30

Pararai, Mavis, Fastel Chipepa, and Bright Forkenberg. "Half Logistic-Topp-Leone Lomax Distribution: Properties and Statistical Inference." Journal of Statistical and Econometric Methods, April 11, 2025, 1–25. https://doi.org/10.47260/jsem/1411.

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A new generalization of the Topp-Leone Lomax distribution was developed. The new distribution is a half logistic transformation of the Topp-Leone Lomax distribution. Some important statistical properties of this new distribution were explored that include raw moments, moment generating function, probability weighted moments, distribution of order statistics, R´enyi entropy, and Shannon entropy. The maximum likelihood estimation (mle) technique was used to estimate the unknown model parameters estimates. Consistency of the mles was assessed via Monte Carlo simulation studies. The mle technique
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BHAT, VILAYAT ALI, and Sudesh Pundir. "Intervened Exponential Distribution: Properties and Applications." Pakistan Journal of Statistics and Operation Research, March 2, 2022, 71–84. http://dx.doi.org/10.18187/pjsor.v18i1.3829.

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This manuscript aims to study the intervention-based probability model. Statistical and reliability properties such as the expressions for, cumulative density function (CDF), mean deviations about mean and median, rth order central and non-central moments, ”generation functions” for moments have been derived. Moreover, the expression for reliability function, hazard rate, reverse hazard rate, aging intensity, mean residual life function, stress-strength reliability, and entropy metrics due to R´enyi and Shannon are also derived. Monte Carlo simulation study performance of maximum likelihood es
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32

MAHMUD, KHALED, Rohayanti Hassan, Muhammad Edzuan Zainodin, Shahreen Kasim, and Johanna Ahmad. "A Novel Framework for Malware Detection UsingEntropy-Based Statistical Features and MachineLearning Models Across File Types." Engineering Research Express, May 8, 2025. https://doi.org/10.1088/2631-8695/add645.

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Abstract As cyber threats continue to evolve, the accurate detection of malicious files has
become increasingly crucial. Traditional approaches often fall short due to limited
adaptability to diverse file types and a high incidence of false predictions. This study
addresses these gaps by systematically evaluating entropy-based features in conjunction
with machine learning (ML) models for malicious file detection. Using diverse file
types—documents, images, and compressed files—we employed byte-level analysis of
each file’s raw stream—without any
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33

Abdelrashied, Mohamed, Ayman Aly, and Mustafa Selim. "Studying Thermal and Dynamical Stability of Interacting Rényi and Tsallis Holographic Dark Energy Models in LTB InhomogeneousUniverse." Research in Astronomy and Astrophysics, December 30, 2024. https://doi.org/10.1088/1674-4527/ada423.

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Abstract This work aims to investigate the different stability conditions of two scenarios
of the inhomogeneous Lemaitre-Tolman-Bond model of the universe with holographic dark
energy. We considered the R´enyi and Tsallis holographic models of interacting dark energy.
These holographic models are investigated using the IR cutoff equals the Hubble horizon.
Various stability conditions of these models have been investigated to understand how far
these models can tell us about the recent and future epochs of the universe in comparison to
the cosmolo
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