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The Dirichlet distribution as a multivariate generalization of the beta distribution is especially important for modeling categorical distributions. Hence, its applications vary within a wide range from modeling cell probabilities of contingency tables to modeling income inequalities. Thus, it is commonly used as the conjugate prior of the multinomial distribution in Bayesian statistics. In this study, the parameters of a bivariate Dirichlet distribution are estimated by entropy formalism. As an alternative to maximum likelihood and the method of moments, two methods based on the principle of maximum entropy are used, namely the ordinary entropy method and the parameter space expansion method. It is shown that in estimating the parameters of the bivariate Dirichlet distribution, the ordinary entropy method and the parameter space expansion method give the same results as the method of maximum likelihood. Thus, we emphasize that these two methods can be used alternatively in modeling bivariate and multinomial Dirichlet distributions. [ABSTRACT FROM AUTHOR]

To alleviate the difficulty of combination explosion, in this work, a generalised equivalent extreme-value event is presented to the problem of multi-component simultaneous failure in system reliability analysis, where m components in total l components are failed simultaneously. Firstly, the generalised equivalent extreme-value event is formulated with rigorous mathematical derivation for single boundary problem. Secondly, based on a mathematical transformation, the generalised equivalent extreme-value event is extended to double boundaries problem. Thirdly, by introducing the point estimation method (PEM) and the principle of maximum entropy to calculate the first four-order statistical moments and the failure probability of the equivalent performance function, an easy-to-implement method is proposed, which is capable of solving the multi-component simultaneous failure problem of static and dynamic systems. Finally, the feasibility of the proposed method is verified through a mathematical example and two engineering examples. The comparison to the Monte Carlo simulation shows that the proposed method is of high precision and high efficiency. [ABSTRACT FROM AUTHOR]

Reliable and easy-to-implement predictions of hydrometeorological variables are important for policymaking and public security. In this study, we developed a probabilistic framework for the description of hydrometeorological high-dimensional dependence and prediction by first-time coupling the principle of maximum entropy (POME) with C-vine copulas (PC). Two case studies with different emphases were investigated to evaluate the application of the PC framework. In the first case, we tested the PC framework based on a one-month-ahead streamflow forecast at the outlet station of the Jinsha River Basin. Results indicated that: (1) the marginal probability distributions or margins derived from optimal-moment-based POME best represented the current state of knowledge compared with those from traditional parametric distributions, and (2) the PC framework produced more skillful forecasts than did the traditional parametric C-vine (TC) and three data-driven models. The second case verified the performance of the PC framework in nationwide summer drought identification. Results of visual comparison of two typical historical summer drought events indicated that the PC framework captured the spatio-temporal characteristics of droughts. The PC framework combines the respective advantages of POME and C-vine copulas, ensuring its potential in higher-dimensional hydrometeorological modeling and flexibility in extending to other fields. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Data Acquisition & Processing / Shu Ju Cai Ji Yu Chu Li is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Gene sets are being increasingly leveraged to make high-level biological inferences from transcriptomic data; however, existing gene set analysis methods rely on overly conservative, heuristic approaches for quantifying the statistical significance of gene set enrichment. We created Nonparametric analytical-Rank-based Enrichment Analysis (NaRnEA) to facilitate accurate and robust gene set analysis with an optimal null model derived using the information theoretic Principle of Maximum Entropy. By measuring the differential activity of ~2500 transcriptional regulatory proteins based on the differential expression of each protein's transcriptional targets between primary tumors and normal tissue samples in three cohorts from The Cancer Genome Atlas (TCGA), we demonstrate that NaRnEA critically improves in two widely used gene set analysis methods: Gene Set Enrichment Analysis (GSEA) and analytical-Rank-based Enrichment Analysis (aREA). We show that the NaRnEA-inferred differential protein activity is significantly correlated with differential protein abundance inferred from independent, phenotype-matched mass spectrometry data in the Clinical Proteomic Tumor Analysis Consortium (CPTAC), confirming the statistical and biological accuracy of our approach. Additionally, our analysis crucially demonstrates that the sample-shuffling empirical null models leveraged by GSEA and aREA for gene set analysis are overly conservative, a shortcoming that is avoided by the newly developed Maximum Entropy analytical null model employed by NaRnEA. [ABSTRACT FROM AUTHOR]

A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of L 2 divergence-free velocity fields, is maximized relative to alternate measures supported over the energy–enstrophy surface. Since thermodynamic equilibrium distributions are characterized by maximum entropy, connections are drawn with stationary statistical solutions of the incompressible Navier–Stokes equations. Special emphasis is on the correspondence with the final statistics described by Kolmogorov's theory of fully developed turbulence. [ABSTRACT FROM AUTHOR]

The Dirichlet distribution as a multivariate generalization of the beta distribution is especially important for modeling categorical distributions. Hence, its applications vary within a wide range from modeling cell probabilities of contingency tables to modeling income inequalities. Thus, it is commonly used as the conjugate prior of the multinomial distribution in Bayesian statistics. In this study, the parameters of a bivariate Dirichlet distribution are estimated by entropy formalism. As an alternative to maximum likelihood and the method of moments, two methods based on the principle of maximum entropy are used, namely the ordinary entropy method and the parameter space expansion method. It is shown that in estimating the parameters of the bivariate Dirichlet distribution, the ordinary entropy method and the parameter space expansion method give the same results as the method of maximum likelihood. Thus, we emphasize that these two methods can be used alternatively in modeling bivariate and multinomial Dirichlet distributions.

Survival analysis, and in particular survival distribution estimation, are important issues in the statistical sciences. Various parametric and nonparametric methods have been proposed to estimate the survival distribution. In this respect, the theoretical survival distributions are specified and their parameters are obtained by methods such as the maximum likelihood estimator and the Bayesian estimator and we can mention to nonparametric methods such as the Kaplan-Meier method, Cox regression and the life table. In addition, another important issue in survival analysis, especially in actuarial and biostatistics, is graduation of data for which smoothness and goodness of fit are two fundamental requirements.On the other hand, in the probability theory, there are two basic approaches to estimate probability distributions by using the concept of entropy: Maximum Entropy Principle (ME) and Minimum Kullback-Leibler Principle (MKL) or Minimum Cross Entropy Principle. In this paper, we examine the approach of the above two optimization models to estimate survival and probability distributions, especially for the classification of the data. In these studies, in addition to investigating parametric models, in order to achieve a compromise between the conditions of smoothness and goodness of fit, we apply a new entropy optimization model by defining an objective function combined from both of the two above principles and adjusting a coefficient that is used to ensure the degree of goodness of fitting and smoothing the estimates, as well as to show their priority in the classification of the data. We use this model to estimate the mortality probability distribution, particularly the column related to the mortality probability of a certain age ( qx) in life table. Finally, with the help of this method, we set the life table for Iranian women and men in 2011../files/site1/files/72/8Abstract.pdf

Gene sets are being increasingly leveraged to make high-level biological inferences from transcriptomic data; however, existing gene set analysis methods rely on overly conservative, heuristic approaches for quantifying the statistical significance of gene set enrichment. We created Nonparametric analytical-Rank-based Enrichment Analysis (NaRnEA) to facilitate accurate and robust gene set analysis with an optimal null model derived using the information theoretic Principle of Maximum Entropy. By measuring the differential activity of ~2500 transcriptional regulatory proteins based on the differential expression of each protein’s transcriptional targets between primary tumors and normal tissue samples in three cohorts from The Cancer Genome Atlas (TCGA), we demonstrate that NaRnEA critically improves in two widely used gene set analysis methods: Gene Set Enrichment Analysis (GSEA) and analytical-Rank-based Enrichment Analysis (aREA). We show that the NaRnEA-inferred differential protein activity is significantly correlated with differential protein abundance inferred from independent, phenotype-matched mass spectrometry data in the Clinical Proteomic Tumor Analysis Consortium (CPTAC), confirming the statistical and biological accuracy of our approach. Additionally, our analysis crucially demonstrates that the sample-shuffling empirical null models leveraged by GSEA and aREA for gene set analysis are overly conservative, a shortcoming that is avoided by the newly developed Maximum Entropy analytical null model employed by NaRnEA.

In this paper a new method of parameter estimation was employed for extended Burr XII parameters using the principle of maximum entropy (POME) based on k-record values. Exact solutions for expectations were obtained. Monte Carlo simulation method were applied to assess the performance of this method. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we present Gibbs' original discussion on the equivalence between equilibrium conditions, i.e., a maximum entropy condition for a given energy and the minimum energy condition for a given entropy - which are presented as theorems by the author. Next, we show how such a discussion appears in contemporary textbooks that present Thermodynamics from its laws (law zero plus the three laws). We compare this presentation with the discussion made by Callen, in his postulational approach to Thermodynamics. We show that part of Gibbs' discussion has been lost even in textbooks dealing with the laws. Furthermore, we argue that Callen's approach does not emphasize the fact that although the principles are the same, thermalizing a system composed of distinct processes (one with constant energy and the other with constant temperature) leads to different temperature values. In addition to solving the problem analytically, we present a graphical analysis of the problem. At the end, we discuss implications for thermodynamics teaching. [ABSTRACT FROM AUTHOR]

An automatic thresholding method based on Shannon entropy difference and dynamic synergic entropy is proposed to select a reasonable threshold from the gray level image with a unimodal, bimodal, multimodal, or peakless gray level histogram. Firstly, a new concept called Shannon entropy difference is proposed, and the stopping condition of a multi-scale multiplication transformation is automatically controlled by maximizing Shannon entropy difference to produce edge images. Secondly, the gray level image is thresholded by the gray levels in order from smallest to largest to generate a series of binary images, followed by extracting contour images from the binary images. Then, a series of gray level histograms that can dynamically reflect gray level distributions and pixel positions are constructed using the edge images and the contour images synergically. Finally, dynamic synergic Shannon entropy is calculated from this series of gray level histograms, and the threshold corresponding to maximum dynamic synergic entropy is taken as the final segmentation threshold. The experimental results on 40 synthetic images and 50 real-world images show that, although the proposed method is not superior to 8 automatic segmentation methods in computational efficiency, it has more flexible adaptivity of selecting threshold and better segmentation accuracy.

The way false discovery rates (FDRs) are used in the analysis of genomics data leads to excessive false positive rates. In this sense, FDRs overcorrect for the excessive conservatism (bias toward false negatives) of methods of adjusting p values that control a family-wise error rate. Estimators of the local FDR (LFDR) are much less biased but have not been widely adopted due to their high variance and lack of availability in software. To address both issues, we propose estimating the LFDR by correcting an estimated FDR or the level at which an FDR is controlled. [ABSTRACT FROM AUTHOR]

Compositional multistability is widely observed in multispecies ecological communities. Since differences in community composition often lead to differences in community function, understanding compositional multistability is essential to comprehend the role of biodiversity in maintaining ecosystems. In community assembly studies, it has long been recognized that the order and timing of species migration and extinction influence structure and function of communities. The study of multistability in ecology has focused on the change in dynamical stability across environmental gradients, and was developed mainly for low‐dimensional systems. As a result, methodologies for studying the compositional stability of empirical multispecies communities are not well developed. Here, we show that models previously used in ecology can be analyzed from a new perspective, the energy landscape, to unveil compositional stability in observational data. To show that our method can be applicable to real‐world ecological communities, we simulated assembly dynamics driven by population‐level processes, and show that results were mostly robust to different simulation assumptions. Our method reliably captured the change in the overall compositional stability of multispecies communities over environmental change, and indicated a small fraction of community compositions that may be channels for transitions between stable states. When applied to murine gut microbiota, our method showed the presence of two alternative states whose relationship changes with age, and suggested mechanisms by which aging affects the compositional stability of the murine gut microbiota. Our method provides a practical tool to study the compositional stability of communities in a changing world, and will facilitate empirical studies that integrate the concept of multistability from different fields. [ABSTRACT FROM AUTHOR]

Internal instability of a soil is closely related to its particle size distribution (PSD) that occurs when its coarser particles cannot protect the finer particles from erosion, thereby inducing permanent changes in its original PSD. This study proposes a new criterion based on grading entropy theory for prompt assessment of internal stability. PSD is discretized into several fractions to extract particle grading information through statistical analysis. Two normalized variables: base entropy ( h 0 ) and entropy increment ( Δ h ) are determined directly from the PSD curve, and the principle of maximum entropy is used to obtain a semi-ellipse within plane formed by h 0 and Δ h , wherein a PSD can be simply expressed as a point. A clear boundary between stable and unstable soils is visualized at maximum Δ h line, which is used to correctly evaluate a large published experimental dataset and its performance is compared with the existing criteria. [ABSTRACT FROM AUTHOR]

The Baranyi--Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, we obtain the Liouville--Gibbs partial differential equation for the probability density function of the two-dimensional solution stochastic process. Because the exact solution of this equation is unaffordable, we use a finite volume scheme to numerically approximate the aforementioned probability density function. From this key information, we design an optimization procedure in order to determine the best growth rates of the Baranyi--Roberts model, so that the expectation of the numerical solution is as close as possible to the sample data. The results evidence good fitting that allows for performing reliable predictions. [ABSTRACT FROM AUTHOR]

The classical kinetic equation has been broadly used to describe reaction and deactivation processes in chemistry. The mathematical formulation of this deterministic nonlinear differential equation depends on reaction and deactivation rate constants. In practice, these rates must be calculated via laboratory experiments, hence involving measurement errors. Therefore, it is more realistic to treat these rates as random variables rather than deterministic constants. This leads to the randomization of the kinetic equation, and hence its solution becomes a stochastic process. In this paper we address the probabilistic analysis of a randomized kinetic model to describe reaction and deactivation by catalase of hydrogen peroxide decomposition at a given initial concentration. In the first part of the paper, we determine closed-form expressions for the probability density functions of important quantities of the aforementioned chemical process (the fractional conversion of hydrogen peroxide, the time until a fixed quantity of this fractional conversion is reached and the activity of the catalase). These expressions are obtained by taking extensive advantage of the so called Random Variable Transformation technique. In the second part, we apply the theoretical results obtained in the first part together with the principle of maximum entropy to model the hydrogen peroxide decomposition and aspergillus niger catalase deactivation using real data excerpted from the recent literature. Our results show full agreement with previous reported analysis but having as additional benefit that they provide a more complete description of both model inputs and outputs since we take into account the intrinsic uncertainties involved in modelling process. [ABSTRACT FROM AUTHOR]

In this paper, we propose a segmentation method based on region growing and evolutionary algorithms. Before segmentation, the number of classes is determined by the principle of maximum entropy. The proposed approach is validated on some synthetic and real images and, it shows to be very interesting as decision support in quality control. [ABSTRACT FROM AUTHOR]

New experimental and numerical techniques constitute the major recent advancements in the study of flow through porous media. However, a model that duly links the micro- and macroscales of this phenomenon is still lacking. Therefore, the present work describes a new, analytical model suitable for both Darcian and post-Darcian flow. Unlike its predecessors, most of which are based on empirical assessments or on some derivation of the Navier–Stokes equations, the presented model employed the principle of maximum entropy, along with a reduced number of premises. Nevertheless, it is compatible with classic expressions, such as Darcy's and Forchheimer's laws. Also, great adherence to previously published experimental results was observed. Moreover, the developed model allows for the delimitation of Darcian and post-Darcian regimes. It enabled the determination of a probabilistic distribution function of flow velocities within the pore space. Further, it bestowed richer interpretations of the physical meanings of principal flow parameters. Finally, through a new quantity called the entropy parameter, the proposed model may serve as a bridge between experimental and numerical findings both at the micro- and macroscales. Therefore, the present research yielded an analytical, entropy-based model for flow through porous media that is sufficiently general and robust to be applied in several fields of knowledge. [ABSTRACT FROM AUTHOR]

We present, an interactive data exploration system that uses a probabilistic approach to generate a small, query-able summary of a dataset. Departing from traditional summarization techniques, we use the Principle of Maximum Entropy to generate a probabilistic representation of the data that can be used to give approximate query answers. We develop the theoretical framework and formulation of our probabilistic representation and show how to use it to answer queries. We then present solving techniques, give two critical optimizations to improve preprocessing time and query execution time, and explore methods to reduce query error. Lastly, we experimentally evaluate our work using a 5 GB dataset of flights within the USA and a 210 GB dataset from an astronomy particle simulation. While our current work only supports linear queries, we show that our technique can successfully answer queries faster than sampling while introducing, on average, no more error than sampling and can better distinguish between rare and nonexistent values. We also discuss extensions that can allow for data updates and linear queries over joins. [ABSTRACT FROM AUTHOR]

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches to it, we show that entropy has a universal stochastic definition, which is not disorder. Hence, we contend that entropy should be used as a mathematical (stochastic) concept as rigorously as possible, free of metaphoric meanings. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept, and promotes entropy as the mother of creativity and evolution. As the social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether maximum entropy, applied to the distribution of a wealth-related variable, namely annual income, can give an objective description. Using publicly available income data, we show that income distribution is consistent with the principle of maximum entropy. The increase in entropy is associated to increases in society’s wealth, yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in the development of and increase in the entropy of income. Such findings are contrary to the theory of ecological economics and other theories that use the term entropy in a Malthusian perspective.

The Baranyi–Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, we obtain the Liouville–Gibbs partial differential equation for the probability density function of the two-dimensional solution stochastic process. Because the exact solution of this equation is unaffordable, we use a finite volume scheme to numerically approximate the aforementioned probability density function. From this key information, we design an optimization procedure in order to determine the best growth rates of the Baranyi–Roberts model, so that the expectation of the numerical solution is as close as possible to the sample data. The results evidence good fitting that allows for performing reliable predictions.

Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there have been criticisms on this thresholding approach such as an inability to filter out spurious correlations, which have led to proposals of alternative methods to overcome some of the problems. We propose a method to create networks from correlation matrices based on optimization with regularization, where we lay an edge between each pair of nodes if and only if the edge is unexpected from a null model. The proposed algorithm is advantageous in that it can be combined with different types of null models. Moreover, the algorithm can select the most plausible null model from a set of candidate null models using a model selection criterion. For three economic datasets, we find that the configuration model for correlation matrices is often preferred to standard null models. For country-level product export data, the present method better predicts main products exported from countries than sample correlation matrices do. [ABSTRACT FROM AUTHOR]

We propose a different way to obtain the distribution of the luminosity function of quasars by using the Principle of Maximum Entropy. The input data come from Richard et al 2006 quasar counts, extending up to redshift 5 and limited from apparent magnitude i  = 15–19.1 at z ≲ 3 to i  = 20.2 for z ≳ 3. Using only few initial data points, the principle allows us to estimate probabilities and hence that luminosity curve. We carry out statistical tests to evaluate our results. The resulting luminosity function compares well to earlier determinations, and our results remain consistent either when the amount or choice of sampled sources is unbiasedly altered. Besides this, we estimate the distribution of the luminosity function for redshifts in which there is only observational data in the vicinity. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to study a generalization of fractional Airy differential equations whose input data (coefficient and initial conditions) are random variables. Under appropriate hypotheses assumed upon the input data, we construct a random generalized power series solution of the problem and then we prove its convergence in the mean square stochastic sense. Afterwards, we provide reliable explicit approximations for the main statistical information of the solution process (mean, variance and covariance). Further, we show a set of numerical examples where our obtained theory is illustrated. More precisely, we show that our results for the random fractional Airy equation are in full agreement with the corresponding to classical random Airy differential equation available in the extant literature. Finally, we illustrate how to construct reliable approximations of the probability density function of the solution stochastic process to the random fractional Airy differential equation by combining the knowledge of the mean and the variance and the Principle of Maximum Entropy. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we propose a segmentation method based on region growing and evolutionary algorithms. Before segmentation, the number of classes is determined by the principle of maximum entropy. The proposed approach is validated on some synthetic and real images and, it shows to be very interesting as decision support in quality control. [ABSTRACT FROM AUTHOR]

We studied the reliability of machine components with parameters that follow an arbitrary statistical distribution using the principle of maximum entropy (PME). We used PME to select the statistical distribution that best fits the available information. We also established a probability density function (PDF) and a failure probability model for the parameters of mechanical components using the concept of entropy and the PME. We obtained the first four moments of the state function for reliability analysis and design. Furthermore, we attained an estimate of the PDF with the fewest human bias factors using the PME. This function was used to calculate the reliability of the machine components, including a connecting rod, a vehicle half-shaft, a front axle, a rear axle housing, and a leaf spring, which have parameters that typically follow a non-normal distribution. Simulations were conducted for comparison. This study provides a design methodology for the reliability of mechanical components for practical engineering projects. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive probabilistic analysis of the deflection of a static cantilever beam based on Euler–Bernoulli's theory. For the sake of generality in our stochastic study, we assume that all model parameters (Young's modulus and the beam moment of inertia) are random variables with arbitrary probability densities, while the loads applied on the beam are described via a delta-correlated process. The probabilistic study is based on the calculation of the first probability density function of the solution and the probability density of other key quantities of interest, such as the shear force, and the bending moment, which are treated as random variables too. To conduct our study, we will first calculate the first moments of the solution, which is a stochastic process, and we then will take advantage of the Principle of Maximum Entropy. Furthermore, we will present an algorithm, based on Monte Carlo simulations, that allows us to simulate our analytical development computationally. The theoretical findings will be illustrated with numerical examples where different realistic probability distributions are assumed for each model random parameter. [ABSTRACT FROM AUTHOR]

Copula functions are widely used to derive multivariate probability distributions in hydrometeorology. One of the key steps in the copula method is the derivation of marginal distributions of individual variables which can be accomplished using the principle of maximum entropy where the distribution parameters are estimated from the specified constraints. This study, investigated two drought variables (severity and duration) by coupling the principle of maximum entropy with parametric and empirical copulas. So, homogeneous climatic zones were first identified by applying the fuzzy clustering method to data from 39 synoptic stations in Iran and then drought severity and duration were determined with the standardized precipitation index. These two variables were scaled and their marginal probability distribution functions were derived using the principle of maximum entropy as well as empirically. Then, the joint probability distribution of drought severity and duration was determined using maximum entropy-copula, and parametric and empirical copulas. Thereafter, bivariate conditional return periods were determined for each homogeneous region. Results showed that 1) univariate and bivariate distributions can be obtained by maximizing entropy; 2) the dependence structure via Spearman's rho, which directly affects the Lagrange parameters of entropy copula, was a controlling factor to optimize the objective function; 3) for a given set of constraints, the maximum entropy copula is independent of the types of marginals; 4)The entropy-entropy copula (with entropy marginals) is considered a better method than alternatives, because it has a similar result to the parametric methods while it only needs to fit a single model. • A Maximum entropy copula method is developed for bivariate drought analysis at homogenous regions of Iran. • The integration of maximum entropy and copula provides a useful method for modeling the dependence structure. • Conditional return period graphs are generated for four homogenous regions using severity and duration drought. • Conditional return period in region I, are significantly greater than other regions. [ABSTRACT FROM AUTHOR]