Search

Here we consider two-parameter and three-parameter versions of the two-tailed quasi-Lindley distribution and investigate their important properties. An attempt has been made to estimate its parameters by the method of maximum likelihood, along with a brief discussion on the existence of the estimators. Further, the distribution is fitted to certain real-life data sets to illustrate the utility of the proposed models. A simulation study is carried out to assess the performance of likelihood estimators of the parameters of the distribution. [ABSTRACT FROM AUTHOR]

We prove that a globally hyperbolic smooth spacetime endowed with a C1-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measure-contraction property. This result includes a class of spacetimes with borderline regularity for which local existence results for the vacuum Einstein equation are known in the setting of spaces with timelike Ricci bounds in a synthetic sense. In particular, these spacetimes satisfy timelike Brunn-Minkowski, Bonnet-Myers, and Bishop-Gromov inequalities in sharp form, without any timelike nonbranching assumption. If the metric is even C1,1, in fact the stronger timelike curvature-dimension condition holds. In this regularity, we also obtain uniqueness of chronological optimal couplings and chronological geodesics. [ABSTRACT FROM AUTHOR]

Dempster-Shafer theory (DST) has attracted wide attention in many fields thanks to its strong advantages over probability theory. Whereas the uncertainty measure of basic belief assignment (BBA) in DST is an open and essential problem. The main goal of this article is to propose a new belief Rényi entropy for the uncertainty measure of BBA, which is inspired by generalized Rényi entropy in DST. The proposed belief Rényi entropy satisfies some desirable properties of uncertainty measure. Furthermore, the proposed belief Rényi entropy can be degraded to Rényi entropy when BBA is transformed into a probability distribution. Finally, a new decision-making method is designed based on the proposed belief Rényi entropy. The validity of the proposed belief entropy is verified by some numerical examples and its application to decision-making. [ABSTRACT FROM AUTHOR]

Renyi entropy-based thresholding is a popular image segmentation method. In this work, to improve the performance of the Renyi entropy thresholding method, an efficient adaptive multilevel Renyi entropy thresholding method based on the energy curve with dynamic programming (DP + ARET) is presented. First, the histogram is substituted by the energy curve in the Renyi entropy thresholding to take advantage of the spatial context information of pixels. Second, an adaptive entropy index selection strategy is proposed based on the image histogram. Finally, to decrease the computation complexity of the multilevel Renyi entropy thresholding, an efficient solution is calculated by the dynamic programming technique. The proposed DP + ARET method can obtain the global optimal thresholds with the time complexity linear in the number of the thresholds. The comparative experiments between the proposed method with the histogram-based method verified the effectiveness of the energy curve. The segmentation results on the COVID-19 Computed Tomography (CT) images with the same objective function by the proposed DP + ARET and swarm intelligence optimization methods testify that the DP + ARET can quickly obtain the global optimal thresholds. Finally, the performance of the DP + ARET method is compared with several image segmentation methods quantitatively and qualitatively, the average segmented accuracy (SA) is improved by 7% than the comparative methods. The proposed DP + ARET method can be used to fast segment the images with no other prior knowledge. [ABSTRACT FROM AUTHOR]

The new continuous class of probability distribution named the Power Burr X-T (PBX-T) family is proposed in this paper. The essential characteristics of the PBX-T family of distributions, i.e. conventional moments and associated procedures, stress-strength reliability, and Rényi entropy, are derived and studied. Some special models belonging to the new family have been comprehensively explored concerning their shapes. Extensive simulations have been conducted to compare the maximum likelihood (ML) estimates with other classical estimators. It is found that the mean squared errors and the bias of the ML estimates are relatively least for large samples. Moreover, real-life applications from medical and engineering fields have been used to demonstrate the potentiality and adequacy of the suggested sub-models from the PBX-T family. The values of observed goodness-of-fit measures show that the sub-models of the suggested family of distributions are superior in adequacy parallel to the other generalized models. [ABSTRACT FROM AUTHOR]

This paper explored the concept of past Rényi entropy within the context of k-record values. We began by introducing a representation of the past Rényi entropy for the n-th lower k-record values, sampled from any continuous distribution function F, concerning the past Rényi entropy of the n-th lower k-record values sampled from a uniform distribution. Then, we delved into the examination of the monotonicity properties of the past Rényi entropy of k-record values. Specifically, we focused on the aging properties of the component lifetimes and investigated how they impacted the monotonicity of the past Rényi entropy. Additionally, we derived an expression for the n-th lower k-records in terms of the past Rényi entropy, specifically when the first lower k-record was less than a specified threshold level, and then investigated several properties of the given formula. [ABSTRACT FROM AUTHOR]

This paper introduces the Log-Expo Inverse Gompertz Distribution (LET-IG) three-parameter distribution and examines some of its mathematical properties. The study derives the density distribution, reliability function, and hazard rate function. It also provides ordinary moments, quantile function, mean residual life, and Renyi entropy. Five estimation methods for the LET-IG distribution based on complete sampling are discussed. A Monte Carlo simulation study is used to calculate the squared bias and variances of the estimates.M. S. Eliwa (2019) [10] introduced and analyzed a novel three-parameter generalized model called the Kumaraswamy inverse Gompertz distribution. In 2021, M. El-Morshedy [9] developed a four-parameter lifetime model known as the exponentiated generalized inverted Gompertz distribution. In 2022, Arun [2] presented the half Cauchy inverse Gompertz distribution, which utilizes the half-Cauchy distribution as its baseline. In the same year, Moustafa [12] examined the inverse Gompertz distribution (IG) and estimated its survival function. T. M. Adegoke (2023) [13] applied the quadratic rank transmutation map scheme to derive the distribution. Additionally, Taiwo et al. (2023) [14] introduced the Topp-Leone Inverse Gompertz Distribution, an extension of the Gompertz distribution aimed at modeling lifetime datasets. Heba (2023) [4] proposed an adaptive Type-II hybrid progressive censoring strategy to enhance the effectiveness of statistical inference.

Random permutation set (RPS) introduces a novel set that considers all subsets with ordered elements from a given set. Each subset with ordered elements represents a permutation event within the permutation event space (PES). The permutation mass function (PMF) represents the chance of occurrence of events in the PES. PES and PMF make up RPS, which contains ordered information and also provides a new insight to consider the uncertainty. This characteristic aligns more closely with the occurrence of ordered events in the real world. However, existing entropies cannot measure the uncertainty with ordered information. To address this issue, a generalized Rényi entropy is proposed, it degenerates into different entropies with the changing of scenarios and parameters, in other words, it is compatible with these entropies. When the events in permutation event space are not ordered, Rényi-RPS entropy degenerates into Deng entropy. In addition, Rényi-RPS entropy further degenerates into Rényi entropy under the probability distribution. In a further way, when the parameter α→1, Rényi-RPS entropy evolves into Shannon entropy. Several numerical examples will illustrate the characteristics of the presented Rényi-RPS entropy. [ABSTRACT FROM AUTHOR]

This paper explored the concept of past Rényi entropy within the context of $ k $-record values. We began by introducing a representation of the past Rényi entropy for the $ n $-th lower $ k $-record values, sampled from any continuous distribution function $ F, $ concerning the past Rényi entropy of the $ n $-th lower $ k $-record values sampled from a uniform distribution. Then, we delved into the examination of the monotonicity properties of the past Rényi entropy of $ k $-record values. Specifically, we focused on the aging properties of the component lifetimes and investigated how they impacted the monotonicity of the past Rényi entropy. Additionally, we derived an expression for the $ n $-th lower $ k $-records in terms of the past Rényi entropy, specifically when the first lower $ k $-record was less than a specified threshold level, and then investigated several properties of the given formula.

This paper introduced and investigated the power unit inverse Lindley distribution (PUILD), a novel two-parameter generalization of the famous unit inverse Lindley distribution. Among its notable functional properties, the corresponding probability density function can be unimodal, decreasing, increasing, or right-skewed. In addition, the hazard rate function can be increasing, U-shaped, or N-shaped. The PUILD thus takes advantage of these characteristics to gain flexibility in the analysis of unit data compared to the former unit inverse Lindley distribution, among others. From a theoretical point of view, many key measures were determined under closed-form expressions, including mode, quantiles, median, Bowley's skewness, Moor's kurtosis, coefficient of variation, index of dispersion, moments of various types, and Lorenz and Bonferroni curves. Some important measures of uncertainty were also calculated, mainly through the incomplete gamma function. In the statistical part, the estimation of the parameters involved was studied using fifteen different methods, including the maximum likelihood method. The invariant property of this approach was then used to efficiently estimate different uncertainty measures. Some simulation results were presented to support this claim. The significance of the PUILD underlying model compared to several current statistical models, including the unit inverse Lindley, exponentiated Topp-Leone, Kumaraswamy, and beta and transformed gamma models, was illustrated by two applications using real datasets.

We introduce a new flexible distribution four-parameter which is called [0,1]Truncated Exponentiated Exponential Burr type X distribution ([0,1] TEE-BX). Using binomial series expansion and exponential expansion, the new distribution is expanded by four parameters. We derive moments, moment generating function, quantile function, order statistics and the Rényi entropy. The maximum likelihood estimation method is used to estimate the parameters of the proposed TEE-BX model [0,1]. Finally, using two real-world data sets, the performance of the [0,1] TEE-BX distribution is explored. Based on the certain goodness of fit criteria, we conclude that the [0,1] TEE-BX distribution has a better fit than the other distributions. [ABSTRACT FROM AUTHOR]

In this work, the holographic dark energy model is constructed by using the non‐extensive nature of the Schwarzschild black hole via the Rényi entropy. Due to the non‐extensivity, the black hole can be stable under the process of fixing the non‐extensive parameter. A change undergoing such a process would then motivate us to define the energy density of the Rényi holographic dark energy (RHDE). As a result, the RHDE with choosing the characteristic length scale as the Hubble radius provides the late‐time expansion without the issue of causality. Remarkably, the proposed dark energy model contains the non‐extensive length scale parameter additional to the standard ΛCDM$\Lambda{\rm CDM}$ model. The cosmic evolution can be characterized by comparing the size of the Universe to this length scale. Moreover, the preferable value of the non‐extensive length scale is determined by fitting the model to recent observations. The results of this work would shed light on the interplay between the thermodynamic description of the black hole with non‐extensivity and the classical gravity description of the evolution of the Universe. [ABSTRACT FROM AUTHOR]

A universal method is proposed for performing calculations within the framework of generalized statistics generated by the parametric Tsallis, Rényi, and Sharma–Mittal entropies. The essence of the approach lies in the use of an auxiliary gamma distribution whose parameters correspond to a particular variant of the statistics. Equations are derived that allow the generalised partition function and the mean energy to be expressed in terms of canonical quantities. The effectiveness of the proposed method is demonstrated using the example of Rényi statistics. The Maxwell–Rényi distribution is obtained and its properties are calculated, based on which assumptions about the possible nature of the generalised parameter are formulated. [ABSTRACT FROM AUTHOR]

The shortest distance between the first $ n $ iterates of a typical point can be quantified with a log rule for some dynamical systems admitting Gibbs measures. We show this in two settings. For topologically mixing Markov shifts with at most countably infinite alphabet admitting a Gibbs measure with respect to a locally Hölder potential, we prove the asymptotic length of the longest common substring for a typical point converges and the limit depends on the Rényi entropy. For interval maps with a Gibbs-Markov structure, we prove a similar rule relating the correlation dimension of Gibbs measures with the shortest distance between two iterates in the orbit generated by a typical point. [ABSTRACT FROM AUTHOR]

The concept of entropy, emerged from thermodynamics and statistical mechanics is of fundamental importance in some scientific and technological areas such as communication theory, physics, probability and statistics. Fuzzy entropy is much looked upon concept for measuring fuzzy information. The concept of fuzzy entropy was firstly mentioned by Zadeh way back in 1965 as a measure of fuzziness. In this paper, we introduce Mathai - Haubold fuzzy entropy with the proof of its validity. In addition, the elegant properties are studied of the proposed fuzzy entropy measure. [ABSTRACT FROM AUTHOR]

We consider two types of entropy, namely, Shannon and Rényi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with intensity. While for Shannon entropy the proof is comparatively simple, for Rényi entropy, which depends on additional parameter α > 0, we can characterize it as nontrivial. The proof is based on application of Karamata’s inequality to the terms of Poisson distribution. [ABSTRACT FROM AUTHOR]

This paper proposed a three parameter Maxwell-Gompertz distribution as an extension of Gompertz distribution. Some statistical properties of the distribution such as moments, survival and hazard functions, quantile function, Rényi entropy and order statistics were derived. Maximum likelihood method was used to estimate the model parameters. A simulation study was carried out in order to gain an insight into the performance on small, moderate and large samples. The flexibility of the new distribution was empirically demonstrated in comparison to four other extensions of Gompertz distributions using two real life datasets. [ABSTRACT FROM AUTHOR]

We show that a unital map between Jordan–Banach algebras or Banach algebras that preserves function calculus given by a single nontrivial locally analytic function must be a Jordan morphism. Ramifications of this results are presented. As an application we prove that quantum channel on general Jordan -algebras preserving Segal and Renyi entropy must be a Jordan homomorphism. [ABSTRACT FROM AUTHOR]

In this paper, we attempted to expand the Frechet distribution by employing the T-X family of distributions and named the newly formulated model Extended odd Frechet-exponential distribution (EOFED). Several structural properties, reliability measurements and characteristics were estimated and discussed. The study presents graphs which depict the behaviour of the probability density function, cumulative distribution function and the hazard rate function. The adaptability and flexibility of this novel distribution were achieved through the application of real-world data sets. A simulation study was performed to evaluate and compare the output efficacy of the estimators. [ABSTRACT FROM AUTHOR]

A new distribution is proposed in this artic;e using the area-biased as a special case of the weighted distributions. It is called the area-bias Benrabia distribution. The properties of this distribution are investigated, including moments, the moment generating function, the reliability functions, and many others. Several numerical studies are carried out, they show that the distribution is right-skewed and leptokurtic. We briefly describe different approaches of estimating the distribution parameters, namely, maximum likelihood, ordinary least-square and weighted least-square, maximum product of spacings, Cramer Von Mises and Anderson-Darling and compare them using extensive numerical simulations. We have shown that the distribution’s parameters are approximately unbiased and consistent. Two real data sets applications are run to show the goodness of fit of the suggested distribution. They illustrate that the proposed distribution fits these data better than other competence distributions.

This article dealt with further properties of the Renyi entropy and the residual Renyi entropy of $ k $-record values. First, we discussed the Renyi entropy order and its connection with the usual stochastic and dispersive orders. We then addressed the monotonicity properties of the residual Renyi entropy of $ k $-records, focusing on the aging properties of the component lifetimes. We also expressed the residual $ n $th upper $ k $-records in terms of Renyi entropy when the first dataset exceeded a certain threshold, and then studied various properties of the given formula. Finally, we conducted a parametric estimation of the Renyi entropy of the $ n $th upper $ k $-records. The estimation was performed using both real COVID-19 data and simulated data.

One of the most popular techniques for changing the purpose of an image or resizing a digital image with content awareness is the seam-carving method. The performance of image resizing algorithms based on seam machining shows that these algorithms are highly dependent on the extraction of importance map techniques and the detection of salient objects. So far, various algorithms have been proposed to extract the importance map. In this paper, a new method based on Rényi entropy is proposed to extract the importance map. Also, a deep learning network has been used to detect salient objects. The simulator results showed that combining Rényi's importance map with a deep network of salient object detection performed better than classical seam-carving and other extended seam-carving algorithms based on deep learning. [ABSTRACT FROM AUTHOR]

A system can be considered to be reliable if it operates successfully for a long period of time and has fewer uncertainties during its lifespan. In other words, lower the uncertainty of a random variable implies higher reliability [see Ebrahimi N. How to measure uncertaintyin the residual life time distribution. Sankhya: Indian J Stat SerA. 1996;58:48–57]. Motivated by this, the present study considers a generalized entropy function, namely the Rényi entropy in the quantile framework as a measure of uncertainty and proposes two nonparametric estimators for its computation. Asymptotic properties of the estimators are established under suitable regularity conditions. Simulation study and real data analysis are carried out to compare the performance and usefulness of the estimators. [ABSTRACT FROM AUTHOR]

This article dealt with further properties of the Renyi entropy and the residual Renyi entropy of k-record values. First, we discussed the Renyi entropy order and its connection with the usual stochastic and dispersive orders. We then addressed the monotonicity properties of the residual Renyi entropy of k-records, focusing on the aging properties of the component lifetimes. We also expressed the residual nth upper k-records in terms of Renyi entropy when the first dataset exceeded a certain threshold, and then studied various properties of the given formula. Finally, we conducted a parametric estimation of the Renyi entropy of the nth upper k-records. The estimation was performed using both real COVID-19 data and simulated data. [ABSTRACT FROM AUTHOR]

This manuscript introduces a novel class of probability distributions termed the New Exponentiated Transformation (NET), aimed at enhancing the flexibility of baseline distributions without adding complexity from extra parameters. The transformation is specialized on the exponentiated exponential distribution, resulting in the New Exponentiated Exponential (NEE) distribution. NEE offers increased flexibility in density function and features hazard rate functions with various shapes. The manuscript also highlights several mathematical properties of proposed distribution. To demonstrate the applicability of the proposed distribution, two engineering data-sets are analyzed, showing that NEE distribution provides a better fit than all other considered models. [ABSTRACT FROM AUTHOR]

The inverse Rayleigh distribution finds widespread applications within life testing and reliability research. Particularly, it proves invaluable in scenarios involving multiple censored data points. In this context, the Renyi, Havrda, Charvat, and Tsallis entropies of the inverse Rayleigh distribution are efficiently calculated. The maximum likelihood approach is used to get the estimators, as well as the approximate confidence interval. The mean squared errors, approximate confidence interval, and their related average length are computed. To illuminate the behavior of estimates across varying sample sizes, a comprehensive simulation study is conducted. The outcomes of the simulation study consistently reveal a downward trend in mean squared errors and average lengths as the sample size increases. Additionally, an interesting finding emerges as the censoring level diminishes. The entropy estimators progressively converge towards their true values. For practical demonstration, the effectiveness of the approach is showcased through the analysis of two real-world datasets. These applications underscore the real-world relevance of the methodology, further validating its utility in addressing complex scenarios involving censored data and inverse Rayleigh distributions. [ABSTRACT FROM AUTHOR]

In compression problems, the minimum average codeword length is achieved by Shannon entropy, and efficient coding schemes such as Arithmetic Coding (AC) achieve optimal compression. In contrast, when minimizing the exponential average length, Rényi entropy emerges as a compression lower bound. This paper presents a novel approach that extends and applies the AC model to achieve results that are arbitrarily close to Rényi’s lower bound. While rooted in the theoretical framework assuming independent and identically distributed symbols, the empirical testing of this generalized AC model on a Wikipedia dataset with correlated symbols reveals significant performance enhancements over its classical counterpart, when considering the exponential average. The paper also demonstrates an intriguing equivalence between minimizing the exponential average and minimizing the likelihood of exceeding a predetermined threshold in codewords’ length. An extensive experimental comparison between generalized and classical AC unveils a remarkable reduction, by several orders of magnitude, in the fraction of codewords surpassing the specified threshold in the Wikipedia dataset.

Radar forward-looking super-resolution imaging is a hot spot in the field of radar imaging research. Restricted by Doppler bandwidth and platform size, traditional high-resolution synthetic aperture imaging and real aperture imaging are not suitable for forward-looking imaging, so a deconvolution-based radar forward-looking super-resolution imaging technology is proposed. The traditional methods currently used in the field of forward-looking deconvolution super-resolution imaging of scanning radar have poor ability to recover the texture details of the target image direction, but simply describe the errors of all measurement data uniformly, which leads to an increase in the result error and have poor ability to adapt to different scenarios. So, this article proposes an improved Tikhonov regularization direction total variation (DTV) deconvolution super-resolution algorithm based on Rayleigh entropy. The algorithm introduces the DTV operator to more accurately restore the edge texture details of the image, and adds a weight matrix to the loss function to more accurately reflect the error degree of each measurement value in the loss function. The entropy enhances the applicability of the algorithm in different scenarios, and significantly improves the radar's ability to recover targets in a low signal-to-noise ratio environment. Finally, the simulation data and measured data processing results show that compared with the traditional method in the field of scanning radar forward looking deconvolution super-resolution imaging, the algorithm proposed in this article is better.

Complex-valued expression models have been widely used in the application of intelligent decision systems. However, there is a lack of entropy to measure the uncertain information of the complex-valued information. Therefore, how to reasonably measure the uncertain information of the complex-valued information is a gap to be filled. In this paper, inspired by the Rényi entropy, we propose the complex-valued Rényi entropy, which measures uncertain information of the complex-valued probability under the framework of complex number, and this is also the first time to measure uncertain information in the complex space. The complex-valued Rényi entropy contains the features of the classical Rényi entropy, i.e., the complex-valued Rényi entropy corresponds to different information functions with different parameters q. Moreover, complex-valued Rényi entropy has some properties, such as non-negativity, monotonicity and etc. Some numerical examples can demonstrate the flexibility and reasonableness of the complex-valued Rényi entropy. [ABSTRACT FROM AUTHOR]

In parametric statistical modeling, it is essential to create generalizations of current statistical distributions that are more flexible when modeling actual data sets. Therefore, this study introduces a new generalized lifetime model named the odd Weibull Inverse Gompertz distribution (OWIG). The OWIG is derived by combining the odd Weibull family of distributions with the inverse Gompertz distribution. Essential statistical properties are discussed, including reliability functions, moments, Rényi entropy, and order statistics. The proposed OWIG is particularly significant as its hazard rate functions exhibit various monotonic and nonmonotonic shapes. This enables OWIG to model different hazard behaviors more commonly observed in natural phenomena. OWIG's parameters are estimated and its flexibility in predicting unique symmetric and asymmetric patterns is shown by analyzing real-world applications from psychology, environmental, and medical sciences. The results demonstrate that the proposed OWIG is an excellent candidate as it provides the most accurate fits to the data compared with some competing models. [ABSTRACT FROM AUTHOR]

One of the most important applications of statistical models is in analyzing survival data. In this study, we developed the Gamma Type Two Half Logistic Topp-Leone-G model using the technique earlier proposed by Zografos and Balakrishnan. Different characteristics of the proposed distribution are obtained. In order to estimate the model parameters based on complete and censored data, the maximum likelihood estimation method is used. Through Monte Carlo simulation, the performance of the estimators is evaluated. The proposed distribution's potential significance and applicability are empirically demonstrated using actual datasets. We found that our new distribution is a very competitive model for describing both complete and censored observations in survival analysis. The work demonstrated that in certain cases, our new model performed better than other parametric models with the same number of parameters. [ABSTRACT FROM AUTHOR]

The random forest algorithm is one of the most popular and commonly used algorithms for classification and regression tasks. It combines the output of multiple decision trees to form a single result. Random forest algorithms demonstrate the highest accuracy on tabular data compared to other algorithms in various applications. However, random forests and, more precisely, decision trees, are usually built with the application of classic Shannon entropy. In this article, we consider the potential of deformed entropies, which are successfully used in the field of complex systems, to increase the prediction accuracy of random forest algorithms. We develop and introduce the information gains based on Renyi, Tsallis, and Sharma-Mittal entropies for classification and regression random forests. We test the proposed algorithm modifications on six benchmark datasets: three for classification and three for regression problems. For classification problems, the application of Renyi entropy allows us to improve the random forest prediction accuracy by 19≥96% in dependence on the dataset, Tsallis entropy improves the accuracy by 20≥98%, and Sharma-Mittal entropy improves accuracy by 22≥111% compared to the classical algorithm. For regression problems, the application of deformed entropies improves the prediction by 2≥23% in terms of R2 in dependence on the dataset. [ABSTRACT FROM AUTHOR]

Topic modeling is a widely used instrument for the analysis of large text collections. In the last few years, neural topic models and models with word embeddings have been proposed to increase the quality of topic solutions. However, these models were not extensively tested in terms of stability and interpretability. Moreover, the question of selecting the number of topics (a model parameter) remains a challenging task. We aim to partially fill this gap by testing four well-known and available to a wide range of users topic models such as the embedded topic model (ETM), Gaussian Softmax distribution model (GSM), Wasserstein autoencoders with Dirichlet prior (W-LDA), and Wasserstein autoencoders with Gaussian Mixture prior (WTMGMM). We demonstrate that W-LDA, WTM-GMM, and GSM possess poor stability that complicates their application in practice. ETM model with additionally trained embeddings demonstrates high coherence and rather good stability for large datasets, but the question of the number of topics remains unsolved for this model. We also propose a new topic model based on granulated sampling with word embeddings (GLDAW), demonstrating the highest stability and good coherence compared to other considered models. Moreover, the optimal number of topics in a dataset can be determined for this model. [ABSTRACT FROM AUTHOR]

AbstractIn analogy with cumulative residual entropy, Di Crescenzo and Longobardi (2009) proposed cumulative past entropy which served as the basis for many following works. To this end, we define cumulative past Renyi entropy for double truncated random variable which we call as interval cumulative past Renyi entropy (ICPRE). Some properties, such as effect of monotone transformation and bounds of ICPRE, are studied. Furthermore, it is shown that the proposed measure uniquely determines the distribution function and characterizes certain lifetime distributions. Finally, non-parametric estimators of ICPRE are obtained and the best proposed estimator is investigated with the help of simulated data set and real-life data set. [ABSTRACT FROM AUTHOR]

The generalized Kaiser–Bessel window function is defined via the modified Bessel function of the first kind and arises frequently in tomographic image reconstruction. In this paper, we study in details the properties of the Kaiser–Bessel distribution, which we define via the symmetric form of the generalized Kaiser–Bessel window function. The Kaiser–Bessel distribution resembles to the Bessel distribution of McKay of the first type, it is a platykurtic or sub-Gaussian distribution, it is not infinitely divisible in the classical sense and it is an extension of the Wigner's semicircle, parabolic and n-sphere distributions, as well as of the ultra-spherical (or hyper-spherical) and power semicircle distributions. We deduce the moments and absolute moments of this distribution and we find its characteristic and moment generating function in two different ways. In addition, we find its cumulative distribution function in three different ways and we deduce a recurrence relation for the moments and absolute moments. Moreover, by using a formula of Ismail and May on quotient of modified Bessel functions of the first kind, we deduce a closed-form expression for the differential entropy. We also prove that the Kaiser–Bessel distribution belongs to the family of log-concave and geometrically concave distributions, and we study in details the monotonicity and convexity properties of the probability density function with respect to the argument and each of the parameters. In the study of the monotonicity with respect to one of the parameters we complement a known result of Gronwall concerning the logarithmic derivative of modified Bessel functions of the first kind. Finally, we also present a modified method of moments to estimate the parameters of the Kaiser–Bessel distribution, and by using the classical rejection method we present two algorithms for sampling independent continuous random variables of Kaiser–Bessel distribution. The paper is closed with conclusions and proposals for future works. [ABSTRACT FROM AUTHOR]

In this article, we present a novel approach to measuring inaccuracy, introducing a two-parametric weighted generalized inaccuracy measure of order α and type β, along with its residual version. Our proposed measure depends on the proportional hazard rate model (PHRM) to uniquely determine the survival function, and we have derived a characterization result for this measure. Through our analysis under the PHRM framework, we have studied various properties of the proposed measure and their interrelationships. [ABSTRACT FROM AUTHOR]

This paper is presenting a new flexible probability distribution which named as Khalil new generalized exponential (KNGEx) distribution. We introduce its mathematical properties. The hazard function of the KNGEx distribution can be increasing, decreasing, and inverted bathtub. The parameters of the distribution are estimated using eight classical methods. Simulation studies based on complete sample are done. Finally, two applications to medicine and engineering data sets are presented. The analyzed data revealed that the proposed distribution could potentially be very useful in describing and modeling both data sets as compared to many other competing distributions. [ABSTRACT FROM AUTHOR]

Velocity distribution plays a fundamental role in understanding the hydrodynamics of open-channel flow. Among a multitude of approaches, the entropy-based approach holds great promise in achieving a reasonable characterisation of the velocity distribution. In entropy-based methods, the distribution depends on a key parameter, known as the entropy parameter (a function of the time-averaged mean velocity and maximum velocity), that relates to channel characteristics, such as channel roughness and channel bed slopes. The entropy parameter was regarded as constant for lack of experimental evidence, which would otherwise demonstrate if it had any correlation with channel properties. A series of experiments were conducted to collect velocity data in the laboratory flume for seven different values of the channel bed slope. The experimental data analysis revealed dissimilar fluctuations in entropy parameter values with varying bed slopes, with the lowest coefficient of variation in Renyi's (∼0.5%) and the highest in Shannon's case (∼10%). Performance evaluation of the predicted results substantiated good accuracy for all three entropies with the best results of Renyi entropy and lent strong support for using a constant (overall average) value of the entropy parameter for a specific channel cross-section rather than separate values for each channel bed slope. HIGHLIGHTS Verification of the influence of the channel bed slope on entropy parameters.; Velocity observations for mild, horizontal, and adverse channel bed slopes.; Shannon, Tsallis, and Renyi entropy-based velocity distributions.; Statistical and experimental evidence supporting the constant nature of all the entropy parameters.; Modified equation to estimate mean and maximum velocity ratio in terms of the Renyi entropy parameter.;

The utilization of automated techniques for processing and analyzing medical images can offer significant support to doctors in their diagnostic and therapeutic practices. This study focuses on the complex task of detecting edges in medical images. To this end, we propose novel multilevel approaches based on quantum image representations of the one-dimensional and two-dimensional histograms of the gray-level distributions. The quantum Rényi entropy is employed to quantify the quantum information present in the two histogram types. The particle swarm optimization algorithm is utilized to identify the optimal threshold values. The performance of the proposed methods is evaluated by comparing them to benchmark methods using a set of medical images. The numerical results substantiate the efficacy of the introduced approaches.

In this paper, the Tsallis and Renyi extropy is presented as a continuous measure of information under the continuous distribution. Furthermore, the features and their connection to other information measures are introduced. Some stochastic comparisons and results on the order statistics and upper records are given. Moreover, some theorems about the maximum Tsallis and Renyi extropy are discussed. On the other hand, numerical results of the non-parametric estimation of Tsallis extropy are calculated for simulated and real data with application to time series model and its forecasting.

This study investigates the detection of two discrete quantum phenomena arising from the interaction between a single two-level atom, SU(1,1)quantum systems, and a graphene membrane in the presence of a laser field. We employ quantum skew information and second-order Rényi entropy as measures to discern non-classicality and entropy, respectively. Two distinct scenarios are considered addressing the system: first, when atomic frequency significantly surpasses laser coupling; second, when the atomic frequency is considerably lower than classical laser coupling. In the former case, both phenomena hinge upon initial preparation conditions for the SU(1,1)coherent cavity, whereas, in the second scenario, the non-classicality and entropy are influenced by the coherent graphene. Notably, we find that the detuning parameter enhances the information of the composite system when the intensities of the coherent cavity and graphene membrane are substantial.

This article presents a method to find the number of topics in Persian research articles, which is actually one of the main challenges in topic modeling. It is the process of automatically recognizing topics in a text with the aim of discovering hidden patterns. This study has estimated the number of topics for Persian research articles using two approaches. The first is based on the greedy search and later uses Renormalization theory, which is a mathematical formalism to construct a procedure for changing the scale of the system so that the behavior of the system preserves. Also, the execution time of both algorithms on Persian academic articles has been compared with each other. The findings indicate that the renormalization approach predicts the number of topics in Persian research articles with the lower time complexity in comparison to the greedy based approach. The approach based on Renormalization has high efficiency for estimating the number of topics in Persian academic articles.

Topic modeling is a widely used instrument for the analysis of large text collections. In the last few years, neural topic models and models with word embeddings have been proposed to increase the quality of topic solutions. However, these models were not extensively tested in terms of stability and interpretability. Moreover, the question of selecting the number of topics (a model parameter) remains a challenging task. We aim to partially fill this gap by testing four well-known and available to a wide range of users topic models such as the embedded topic model (ETM), Gaussian Softmax distribution model (GSM), Wasserstein autoencoders with Dirichlet prior (W-LDA), and Wasserstein autoencoders with Gaussian Mixture prior (WTM-GMM). We demonstrate that W-LDA, WTM-GMM, and GSM possess poor stability that complicates their application in practice. ETM model with additionally trained embeddings demonstrates high coherence and rather good stability for large datasets, but the question of the number of topics remains unsolved for this model. We also propose a new topic model based on granulated sampling with word embeddings (GLDAW), demonstrating the highest stability and good coherence compared to other considered models. Moreover, the optimal number of topics in a dataset can be determined for this model.