Logistic Mixture Model Research Articles

Data-driven Approximation of Cumulative Distribution Function Using Particle Swarm Optimization based Finite Mixtures of Logistic Distribution

This paper proposes a data-driven approximation of the Cumulative Distribution Function using the Finite Mixtures of the Cumulative Distribution Function of Logistic distribution. Since it is not possible to solve the logistic mixture model using the Maximum likelihood method, the mixture model is modeled to approximate the empirical cumulative distribution function using the computational intelligence algorithms. The Probability Density Function is obtained by differentiating the estimate of the Cumulative Distribution Function. The proposed technique estimates the Cumulative Distribution Function of different benchmark distributions. Also, the performance of the proposed technique is compared with the state-of-the-art kernel density estimator and the Gaussian Mixture Model. Experimental results on κ−μ distribution show that the proposed technique performs equally well in estimating the probability density function. In contrast, the proposed technique outperforms in estimating the cumulative distribution function. Also, it is evident from the experimental results that the proposed technique outperforms the state-of-the-art Gaussian Mixture model and kernel density estimation techniques with less training data.

Probabilistic optimal power flow computation for power grid including correlated wind sources

AbstractThis paper sets out to develop an efficient probabilistic optimal power flow (POPF) algorithm to assess the influence of wind power on power grid. Given a set of wind data at multiple sites, their marginal distributions are fitted by a newly developed generalized Johnson system, whose parameters are specified by a percentile matching method. The correlation of wind speeds is characterized by a flexible Liouville copula, which allows to model the asymmetric dependence structure. In order to improve the efficiency for solving POPF problem, a lattice sampling method is developed to generate wind samples at multiple sites, and a logistic mixture model is proposed to fit distributions of POPF outputs. Finally, case studies are performed, the generalized Johnson system is compared with Weibull distribution and the original Johnson system for fitting wind samples, Liouville copula is compared against Archimedean copula for modelling correlated wind samples, and lattice sampling method is compared with Sobol sequence and Latin hypercube sampling for solving POPF problem on IEEE 118‐bus system, the results indicate the higher accuracy of the proposed methods for recovering the joint cumulative distribution function of correlated wind samples, as well as the higher efficiency for calculating statistical information of POPF outputs.

Determination of Kinetic and Thermodynamic Parameters of Biomass Gasification with TG-FTIR and Regression Model Fitting

In this study, the decomposition of five different raw materials (maize, wheat and piney biomass, industrial wood chips and sunflower husk) were investigated using the TG-FTIR method to obtain raw data for model-based calculations. The data obtained from the thermogravimetric analysis served as a basis for kinetic analysis with three different isoconversional, model-free methods, which were the KAS, FWO and Friedman methods. Afterwards, the activation energy and the pre-exponential factor were determined, and no significant difference could be identified among the used methods (difference was under 5%), achieving 203–270 kJ/mol of Ea on average. Thereafter, the thermodynamic parameters were studied. Based on the TG-FTIR data, a logistic regression model was fitted to the data, which gives information about the thermal degradation and the obtained components with different heating rates. The FTIR analysis resulted in differential peaks corresponding to the studied components that were detected within the temperature range of 350–380 °C. The primary degradation processes occurred within a broader temperature range of 200–600 °C. Accordingly, in this work, the use of logistic mixture models as an alternative to traditional kinetic models for the description of the TGA process was also investigated, reaching adequate performance in fitting by a validation data coefficient of determination of R2 = 0.9988.

Complementary use of generalized logistic mixture model and distributed activation energy model in exploring kinetic mechanisms of wheat straw and torrefied rice husk pyrolysis

Lignocellulosic biomass pyrolysis is a multi-step overlapping process, which leads to some difficulties in exploring biomass pyrolysis mechanisms. A kinetic approach combining the generalized logistic mixture model (GLMM) and the distributed activation energy model (DAEM) was proposed to explore the kinetic mechanisms of lignocellulosic biomass pyrolysis. The pyrolysis process of wheat straw could be effectively deconvoluted into three sub-processes by the GLMM, which corresponded to the thermal decomposition of pseudo-hemicellulose, pseudo-cellulose, and pseudo-lignin, respectively. These sub-processes could be adequately represented by the DAEMs and their activation energy distributions peaked at 164.2 kJ mol−1 (with a standard deviation of 2.6 kJ mol−1), 173.4 kJ mol−1 (with a standard deviation of 1.0 kJ mol−1) and 185.1 kJ mol−1 (with a standard deviation of 27.4 kJ mol−1). However, the pyrolysis process of torrefied rice husk was described by two sub-processes corresponding to the thermal decomposition of pseudo-cellulose and pseudo-lignin, with their activation energies peaked at 173.5 kJ mol−1 (with a standard deviation of 2.8 kJ mol−1) and 164.0 kJ mol−1 (with a standard deviation of 12.9 kJ mol−1). The combination of the GLMM and DAEM could provide a methodological guideline to obtain the detailed reactivity distributions involved in biomass pyrolysis, facilitating the optimization of biomass pyrolysis processes and subsequently extending the efficient and clean use of biomass for biofuel production.

Estimation Using Suggested EM Algorithm Based on Progressively Type-II Censored Samples from a Finite Mixture of Truncated Type-I Generalized Logistic Distributions with an Application

In this paper, the identifiability property has been studied for a suggested truncated type-I generalized logistic mixture model which is denoted by TTIGL . A suggested form of the EM algorithm has been applied on type-II progressive censored samples to obtain the maximum likelihood estimates MLE ′ s of the parameters, survival function SF , and hazard rate function HRF of the studied mixture model. Monte Carlo simulation algorithm has been applied to study the behavior of the mean squares errors MSE ′ s of the estimates. Also, a comparative study is conducted between the suggested EM algorithm and the ordinary algorithm of maximizing the likelihood function, which depends on the differentiation of the log likelihood function. The results of this paper have been applied on a real dataset as an application.

Exploring kinetic mechanisms of biomass pyrolysis using generalized logistic mixture model

Pyrolysis is one of promising possible paths for converting waste biomass to heat, bio-fuels, or higher value chemicals. The pyrolysis of biomass involves several overlapping processes due to its complex composition and the complexity of pyrolysis reactions. The characterization and applicability of the generalized logistic mixture model in the kinetic analysis of simulated processes and lignocellulosic biomass pyrolysis processes were investigated. The generalized logistic model showed asymmetrical kinetic profiles, which could fit the simulated DAEM and parallel processes more accurately than the logistic and Weibull models. The pyrolysis kinetic data of xylan, cellulose and lignin could be accurately described by the generalized logistic model with a single component. The pyrolysis kinetics of raw and acid-infused corn stovers was well fitted by the generalized logistic mixture model with three components, and the characterization of individual sub-processes separated from the model could reflect the acid infusion mechanism of corn stover. The generalized logistic mixture model effectively separated the pyrolysis process of raw and acid-washed cotton stalk into three sub-processes, and the kinetic analysis of individual sub-processes using the Friedman isoconversional method showed that those separated sub-processes corresponded to the thermal decomposition of pseudo-components of hemicellulose, cellulose and lignin. Acid washing could reduce the fraction of pseudo-hemicellulose, and increase the pseudo-lignin fraction according to the results from the generalized logistic mixture model. The generalized logistic mixture model enables us to obtain the further kinetic information of the individual processes for lignocellulosic biomass pyrolysis.

Identifying the presence of bacteria on digital images by using asymmetric distribution with k-means clustering algorithm.

This paper is mainly aimed at the decomposition of image quality assessment study by using Three Parameter Logistic Mixture Model and k-means clustering (TPLMM-k). This method is mainly used for the analysis of various images which were related to several real time applications and for medical disease detection and diagnosis with the help of the digital images which were generated by digital microscopic camera. Several algorithms and distribution models had been developed and proposed for the segmentation of the images. Among several methods developed and proposed, the Gaussian Mixture Model (GMM) was one of the highly used models. One can say that almost the GMM was playing the key role in most of the image segmentation research works so far noticed in the literature. The main drawback with the distribution model was that this GMM model will be best fitted with a kind of data in the dataset. To overcome this problem, the TPLMM-k algorithm is proposed. The image decomposition process used in the proposed algorithm had been analyzed and its performance was analyzed with the help of various performance metrics like the Variance of Information (VOI), Global Consistency Error (GCE) and Probabilistic Rand Index (PRI). According to the results, it is shown that the proposed algorithm achieves the better performance when compared with the previous results of the previous techniques. In addition, the decomposition of the images had been improved in the proposed algorithm.

A Robust High-Dimensional Estimation of Multinomial Mixture Models

In this paper, we are concerned with a robustifying high-dimensional (RHD) structured estimation in finite mixture of multinomial models. This method has been used in many applications that often involve outliers and data corruption. Thus, we introduce a class of the multinomial logistic mixture models for dependent variables having two or more discrete categorical levels. Through the optimization with the expectation maximization (EM) algorithm, we study two distinct ways to overcome sparsity in finite mixture of the multinomial logistic model; i.e., in the parameter space, or in the output space. It is shown that the new method is consistent for RHD structured estimation. Finally, we will implement the proposed method on real data.

An artificial-vision- and statistical-learning-based method for studying the biodegradation of type I collagen scaffolds in bone regeneration systems.

This work proposes a method based on image analysis and machine and statistical learning to model and estimate osteocyte growth (in type I collagen scaffolds for bone regeneration systems) and the collagen degradation degree due to cellular growth. To achieve these aims, the mass of collagen -subjected to the action of osteocyte growth and differentiation from stem cells- was measured on 3 days during each of 2 months, under conditions simulating a tissue in the human body. In addition, optical microscopy was applied to obtain information about cellular growth, cellular differentiation, and collagen degradation. Our first contribution consists of the application of a supervised classification random forest algorithm to image texture features (the structure tensor and entropy) for estimating the different regions of interest in an image obtained by optical microscopy: the extracellular matrix, collagen, and image background, and nuclei. Then, extracellular-matrix and collagen regions of interest were determined by the extraction of features related to the progression of the cellular growth and collagen degradation (e.g., mean area of objects and the mode of an intensity histogram). Finally, these critical features were statistically modeled depending on time via nonparametric and parametric linear and nonlinear models such as those based on logistic functions. Namely, the parametric logistic mixture models provided a way to identify and model the degradation due to biological activity by estimating the corresponding proportion of mass loss. The relation between osteocyte growth and differentiation from stem cells, on the one hand, and collagen degradation, on the other hand, was determined too and modeled through analysis of image objects’ circularity and area, in addition to collagen mass loss. This set of imaging techniques, machine learning procedures, and statistical tools allowed us to characterize and parameterize type I collagen biodegradation when collagen acts as a scaffold in bone regeneration tasks. Namely, the parametric logistic mixture models provided a way to identify and model the degradation due to biological activity and thus to estimate the corresponding proportion of mass loss. Moreover, the proposed methodology can help to estimate the degradation degree of scaffolds from the information obtained by optical microscopy.

Regional Decomposition of Images using Three Parameter Logistic Type Mixture Model with K-Means

Regional Decomposition of Images using Three Parameter Logistic Type Mixture Model with K-Means

Isoconversional kinetic analysis of sweet sorghum bagasse pyrolysis by modified logistic mixture model

In order to overcome the noise problem when analyzing the experimental thermogravimetric analysis data and obtain the temperature values at different heating rates for various conversions, a modified logistic mixture model, the combination of two modified logistic functions and a constant, has been presented for fitting all thermogravimetric analysis curves at different heating rates. The thermogravimetric analysis curves of sweet sorghum bagasse pyrolysis at three heating rates of 15, 25 and 35 K min−1 were analyzed. The modified logistic mixture model and logistic mixture model were used for fitting the experimental thermogravimetric analysis curves at all heating rates. The results have shown that the modified logistic mixture model fitted the experimental data better than the logistic mixture model. Making use of the data calculated by the modified logistic mixture model, the effective activation energy values as a function of conversion were obtained by means of the Friedman isoconversional method. The effective activation energies varied from 150 to 320 kJ mol−1 when the conversion ranged from 0.05 to 0.85, which indicated that the pyrolysis of sweet sorghum bagasse was a complex process.

Practical approaches for design and analysis of clinical trials of infertility treatments: crossover designs and the Mantel-Haenszel method are recommended.

Crossover designs have some advantages over standard clinical trial designs and they are often used in trials evaluating the efficacy of treatments for infertility. However, clinical trials of infertility treatments violate a fundamental condition of crossover designs, because women who become pregnant in the first treatment period are not treated in the second period. In previous research, to deal with this problem, some new designs, such as re-randomization designs, and analysis methods including the logistic mixture model and the beta-binomial mixture model were proposed. Although the performance of these designs and methods has previously been evaluated in large-scale clinical trials with sample sizes of more than 1000 per group, the actual sample sizes of infertility treatment trials are usually around 100 per group. The most appropriate design and analysis for these moderate-scale clinical trials are currently unclear. In this study, we conducted simulation studies to determine the appropriate design and analysis method of moderate-scale clinical trials for irreversible endpoints by evaluating the statistical power and bias in the treatment effect estimates. The Mantel-Haenszel method had similar power and bias to the logistic mixture model. The crossover designs had the highest power and the smallest bias. We recommend using a combination of the crossover design and the Mantel-Haenszel method for two-period, two-treatment clinical trials with irreversible endpoints.

Optimizing fitting parameters in thermogravimetry

This study presents an alternative to simple estimation of parametric fitting models used in thermal analysis. The addressed problem consists in performing an alternative optimization method to fit thermal analysis curves, specifically TG curves and their first derivatives. This proposal consists in estimating the optimal parameters corresponding to fitting kinetic models applied to thermogravimetric (TG) curves, using evolutionary algorithms: differential evolution (DE), simulated annealing and covariance matrix adapting evolutionary strategy. This procedure does not need to include a vector with the initial values of the parameters, as is currently required. Despite their potential benefits, the application of these methods is by no means usual in the context of thermal analysis curve’s estimation. Simulated TG curves are obtained and fitted using a generalized logistic mixture model, where each logistic component represents a thermal degradation process. The simulation of TG curves in four different scenarios taking into account the extent of processes overlapping allows us to evaluate the final results and thus to validate the proposed procedure: two degradation processes non-overlapped simulated using two generalized logistics, two processes overlapped, four processes non-overlapped and four processes overlapped two by two. The mean square error function is chosen as objective function and the above algorithms have been applied separately and together, i.e., taking the final solution of the DE algorithm is the initial solution of the remaining. The results show that the evolutionary algorithms provide a good solution for adjusting simulated TG curves, better than that provided by traditional methods.

Thermal characterization of ammonium alum

Thermal decomposition of ammonium alum was studied by simultaneous thermogravimetry (TG)-differential scanning calorimetry (DSC) attached to a Fourier transform infrared (FTIR) spectrometer, so that each mass loss was related with the simultaneous endo- or exothermal behavior and to the FTIR absorption produced by the evolved gases. Apart from some clear dehydration and desulfation processes, other overlapping peaks were observed by DSC, TG, and FTIR. Optimal fitting to logistic mixture models was performed to separate the overlapping processes. Deconvolution of overlapping DTG peaks resulted in single constituent peaks, which were related to plots of some specific FTIR bands along time. Thus, a more accurate insight of the chemical processes taking place was obtained.

Functional Mapping Model of Quantitative Trait Loci in a Full-sib Family

Functional mapping of quantitative trait loci (QTL) has embedded the biological mechanisms and processes of dynamic traits in the statistical method of QTL mapping. Although the statistical model for functional mapping has been well developed in inbred lines, it has not been proposed in a full-sib family, in which the number of alleles may vary over loci and the linkage phases are usually unknown between loci. Since forest trees have several unique biological characteristics and most of them are outbred species, we should not directly apply the functional mapping model for inbred species to them. The objective of this study is to develop a functional mapping statistical model for a full-sib family in forest trees. We suppose that the QTL genotype of one parent is heterozygous but the other is homozygous, and consider all pairwise combinations of marker segregation types and all possible linkage phases between mark loci in a diploid full-sib family into our model. A maximum­ likelihood approach based on a logistic-mixture model, implemented with EM algorithm, was developed to provide the estimation of QTL positions and the parameters responsible for growth trajectories. The results of a large number of simulations showed that our model was robust for identifying the QTL position and estimating the parameters of QTL effects and residual (co)variance.

Weibull mixture model for isoconversional kinetic analysis of biomass oxidative pyrolysis

Abstract In this work, the possibility of applying the weighted sum of three cumulative Weibull distribution functions for the fitting of the kinetic conversion data of biomass oxidative pyrolysis has been investigated. The kinetic conversion data of the thermal decomposition of olive oil solid waste in oxygen atmosphere for different heating rates have been analysed. The results have shown that the experimental data can be perfectly reproduced by the general fitting function. Therefore, it is possible to obtain the corresponding conversion rates of biomass oxidative pyrolysis by differentiating directly the fitted kinetic conversion data. Additionally, the logistic mixture model has been applied to the same experimental data. It can be found that the newly proposed function can provide a better fit of the data than the logistic mixture model. Based on the fitting of Weibull mixture model, the kinetic triples, i.e. E, A and f(α), of oxidative pyrolysis of olive solid waste, were obtained by means of Fried...

Clustering of temporal profiles using a Bayesian logistic mixture model: Analyzing groundwater level data to understand the characteristics of urban groundwater recharge

The hydrogeologic conditions of groundwater can be examined by carefully studying the patterns of fluctuations in groundwater levels. These fluctuations are spatially and temporally influenced by many complicated factors, including rainfall, topography, land use, and hydraulic properties of soils and bedrock (i.e., aquifers). In this article we report a methodology based on the Bayesian logistic mixture model to simultaneously cluster profiles of groundwater level changes over time and estimate the relationships between the characteristics of each cluster and environmental variables. We apply the proposed method to analyze groundwater level profiles from 37 monitoring wells in Seoul, South Korea, and we find four clusters of wells. Using the estimated relationship between the clusters and the environmental variables, we discern the hydrogeologic conditions of each cluster, thus gaining insight into the recharge and subsurface flow of bedrock groundwater in an urban setting and the vulnerability of groundwater to the inflow of potential pollutants from ground surface. This article has supplementary material online.

Kinetic Analysis of Wheat Straw Oxidative Pyrolysis Using Thermogravimetric Analysis: Statistical Description and Isoconversional Kinetic Analysis

The oxidative pyrolysis kinetics of wheat straw was studied by thermogravimetric analysis (TGA) under oxygen dynamic atmosphere. Nonisothermal TGA data at three heating rates of 5, 10, and 20 K min−1 were analyzed. The kinetic conversion data calculated from the TGA data were fitted by the Weibull and logistic mixture models, and the corresponding statistical analyses were performed. The statistical results showed that the Weibull mixture model fitted the experimental data better than the logistic mixture model and can accurately reproduce the kinetic conversion data. Making use of the data predicted by the Weibull mixture model, some data required in the isoconversional kinetic analysis, such as α vs Tα, can be easily obtained. An iterative linear integral isoconversional method was developed and applied to evaluate the activation energy of the oxidative pyrolysis process of wheat straw. The Vyazovkin−Dollimore nonlinear integral isoconversional method was also used to calculate the activation energy. The results have shown that two isoconversional methods are equivalent for the estimation of the activation energy and the obtained activation energy is significantly dependent upon conversion for the oxidative pyrolysis process of wheat straw.

Study of the Degradation of a Polyesther-Polyurethane by TGA and the Logistic Mixture Model

The logistic mixture model was successfully studied previously in the separation of overlapping steps in some polymeric systems by the authors. In the present work, this method is applied to a polyesther-polyurethane degradation under air and inert atmospheres at several heat rates (5, 10, 15, 20 and 25 °C/min) in dynamic TGA. Every logistic component is fitted by reaction order, Johnson-Mehl-Avrami and Sestak-Berggren kinetics equations in order to calculate its kinetic parameters (activation energy, frequency factor and exponents). The reaction order model gives a good fitting and reproduces accurtelly the experimental curves. Johnson-Mehl-Avrami and Sestak- Berggren equations resulted to be not suitables because of the activation energy values obtained.

A logistic mixture model for a family-based association study

A family-based association study design is not only able to localize causative genes more precisely than linkage analysis, but it also helps explain the genetic mechanism underlying the trait under study. Therefore, it can be used to follow up an initial linkage scan. For an association study of binary traits in general pedigrees, we propose a logistic mixture model that regresses the trait value on the genotypic values of markers under investigation and other covariates such as environmental factors. We first tested both the validity and power of the new model by simulating nuclear families inheriting a simple Mendelian trait. It is powerful when the correct disease model is specified and shows much loss of power when the dominance of a model is inversely specified, i.e., a dominant model is wrongly specified as recessive or vice versa. We then applied the new model to the Genetic Analysis Workshop (GAW) 15 simulation data to test the performance of the model when adjusting for covariates in the case of complex traits. Adjusting for the covariate that interacts with disease loci improves the power to detect association. The simplest version of the model only takes monogenic inheritance into account, but analysis of the GAW simulation data shows that even this simple model can be powerful for complex traits.