Matrixdist: an R package for statistical analysis of matrix distributions

Distribution mixtures are used as models to analyze grouped data. The estimation of parameters is an important step for mixture distributions. The latent class model is generally used as the analysis of mixture distributions for discrete data. In this paper, we consider the parameter estimation for a mixture of logistic regression models. We know that the expectation maximization (EM) algorithm was most used for estimating the parameters of logistic regression mixture models. In this paper, we propose a new type of fuzzy class model and then derive an algorithm for the parameter estimation of a fuzzy class logistic regression model. The effects of the explanatory variables on the response variables are described. The focus is on binary responses for the logistic regression mixture analysis with a fuzzy class model. An algorithm, called a fuzzy classification maximum likelihood (FCML), is then created. The mean squared error (MSE) based accuracy criterion for the FCML and EM algorithms to the parameter estimation of logistic regression mixture models are compared using the samples drawn from logistic regression mixtures of two classes. Numerical results show that the proposed FCML algorithm presents good accuracy and is recommended as a new tool for the parameter estimation of the logistic regression mixture models.

Using general regression with local tuning for learning mixture models from incomplete data sets

EM algorithm using overparameterization for the multivariate skew-normal distribution

HLA Alleles and Haplotypes Frequency in the Population of the Republic of Tatarstan, Russia

In this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method of Marshall and Olkin (1967) which has natural interpretations, and it can be applied in fatal shock models or in competing risks models. In the second model, the proposed method of Marshall and Olkin (1997) is generalized to bivariate case and a new bivariate distribution is introduced. We call these new distributions as the bivariate Gompertz (BGP) distribution and bivariate Gompertz-geometric (BGPG) distribution, respectively. Moreover, the BGP model can be obtained as a special case of the BGPG model. Then, we present various properties of the new bivariate models. In this regard, the joint and conditional density functions, the joint cumulative distribution function can be obtained in compact forms. Also, the aging properties and the bivariate hazard gradient are discussed. This model has five unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze three real data sets for illustrative purposes.

Mixture distribution and multifractal analysis applied to wind speed in the Brazilian Northeast region

On-board train control equipment is the core equipment to ensure the safety and smooth operation of the train, the prognostics and health management for on-board equipment(OBE) has great significance. In this paper, aiming at the uncertainty of OBE failure and under the circumstances of less failure samples, puts forward that regard the whole OBE as a black box, the analysis and prediction of time between failures is conducted. Firstly, through the statistical analysis of the train operation fault log files, the sample series of time between failures(TBF) is obtained. The statistical distribution analysis is performed for the sample series, and the Weibull distribution model is established and tested, it shows that it has certain rules and can be predicted. Finally, TBF is used for short time prediction based on grey support vector machine, the accuracy of general and serious faults are 86.87% and 90.04% respectively by example verification, it shows that this method has good predictive effect, the prediction results have certain guiding significance for CBM.

Data analysis and graphical representation form an essential part of scientific research dissemination. The life-science community is moving towards a more transparent presentation of single data points or data distributions and away from mean values displayed as bar charts. To facilitate transparent data display to the mycorrhiza community, we present “Ramf” an open-source R package for statistical analysis and preparation of a variety of publication-ready plots, custom-made for analyzing and displaying quantitative root colonization by arbuscular mycorrhiza fungi or any kind of data to be displayed in the same format. Ramf replaces the scripting needed for data analysis and can be readily used by researchers not acquainted with R. In addition, the package is open to improvements by the community. Ramf is available at https://github.com/mchiapello/Ramf.

Background . Properly constructed decision support systems (DSS) for modelling and forecasting behaviour of dynamic systems provide a possibility for taking into consideration uncertainties of probabilistic, statistical and structural types what results in higher quality of developed models and estimated forecasts. Objective . To consider general reasons for loosing (missing) data in statistical data analysis; to provide categorization of missing data into several groups, and identify the reasons for missing measurements; to provide stepwise system methodology for uncertainty analysis and selection of data imputation techniques; to give an insight into some popular missing values imputation techniques regarding their possible applications. Methods . To solve the problems mentioned the following methods have been used: data categorization approach from business or practical point of view that is necessary for discovering the reasons for availability of systemic and/or random missing values; the modern systemic methodology was hired for analysis of uncertainty causes and missing values imputation; the decision tree based imputation procedures; EM algorithm and regression model approach to forecasting missing data using forecasting functions. Results . The main results of the study are in categorization of the missing data into groups; development of systemic methodology for analysis of uncertainty causes and missing values imputation; providing an analysis for possibilities of missing values imputation with decision trees, EM algorithm and regression models; development of multistep forecasting functions on the basis of autoregression models; illustration of application of some selected perspective methods for missing data imputation. Conclusions . We proposed the six steps system methodology for data imputation which stresses that selection of correct method for imputation is tightly connected with the step-by-step analysis of the gaps causes and finding an appropriate technique for their imputation. The results of imputation sometimes are rather far from the existing data and should be smoothed or even broken from the sample due to their incorrectness. For such cases it should be proposed a new probabilistic-regression method which allows define parameters of the probability interval for the regression aiming missing data imputation. A series of computing experiments performed with EM algorithm, forecast regression based imputation technique and some other approaches shows that it is possible to reach high quality results regarding correct processing of data with missing values.

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.

The purpose of this study was to investigate the validity of exploratory factor analysis (EFA) study on the work attributes of pharmaceutical sales executives in Nigeria using confirmatory factor analysis (CFA), and furthermore to evaluate the relative importance of the work attributes. An analytical study design used a 13-item, 5-point Likert scale questionnaire administered to 226 pharmaceutical sales executives using a simple random sampling method. Data analysis using the Statistical Package for Social Sciences (SPSS) and Analysis of Moment Structures (AMOS) with a significance level set at p<0.05. The measurement model was evaluated using the maximum likelihood method. Model fit criteria measures for CFA were satisfactory (CMIN/df=2.297; NFI=0.017; TLI=0.905; CFI=0.950; RMSEA=0.064). The study showed that the most dominant attribute was involvement in community education programs with a regression coefficient of 0.892, and the least was limited access to customers (0.446). Convergent validity measures were acceptable. Divergent validity can be enhanced by including more items. The study confirmed the validity of the EFA study outcomes obtained from the previous research work. The purpose of this study was to investigate the validity of exploratory factor analysis (EFA) study on the work attributes of pharmaceutical sales executives in Nigeria using confirmatory factor analysis (CFA), and furthermore to evaluate the relative importance of the work attributes. An analytical study design used a 13-item, 5-point Likert scale questionnaire administered to 226 pharmaceutical sales executives using a simple random sampling method. Data analysis using the Statistical Package for Social Sciences (SPSS) and Analysis of Moment Structures (AMOS) with a significance level set at p<0.05. The measurement model was evaluated using the maximum likelihood method. Model fit criteria measures for CFA were satisfactory (CMIN/df=2.297; NFI=0.017; TLI=0.905; CFI=0.950; RMSEA=0.064). The study showed that the most dominant attribute was involvement in community education programs with a regression coefficient of 0.892, and the least was limited access to customers (0.446). Convergent validity measures were acceptable. Divergent validity can be enhanced by including more items. The study confirmed the validity of the EFA study outcomes obtained from the previous research work.

Arterial smooth muscle cells in contractile and synthetic state were analyzed by optical diffractometry. Cell sections (80-90 nm) were photographed in an electron microscope and diffraction patterns of the plates (negatives) were produced using a helium-neon laser. Radial and angular distributions of light intensity in the diffractograms were measured and digitized using an electronic detector plate consisting of ring- and wedge-shaped photosensitive elements; radial distributions provide information about size of structures and distances between them and angular distributions about spatial orientation of structures in the images. Micrographs of nuclei and cytoplasm were analyzed separately (40-50 plates in each group). Computerized statistical analysis of radial distributions of light intensity showed that the nuclear chromatin pattern differed between cells in contractile and synthetic state. The probability that the observed difference could have arisen purely by chance was less than 10(-5). Computer-aided classification to the a priori known cell group was correct in 96.5% of the cases. Analysis of radial distributions of light intensity similarly showed marked differences in cytoplasmic structure between cells in contractile state (dominated by bundles of myofilaments) and synthetic state (dominated by cisternae of rough endoplasmic reticulum). The probability that the observed difference could have arisen purely by chance was less than 10(-5). Computer-aided classification to the a priori known cell group was correct in 92.0% of the cases. In contrast, analysis of angular distributions of light intensity did not indicate any statistically significant differences between contractile and synthetic state cells. A likely reason is that both myofilaments and cisternae of rough endoplasmic reticulum were arranged in parallel. The results demonstrate that optical diffractometry is a useful method for image analysis in studies of cell fine structure. It provides information about size and orientation of structures with poorly defined shape and is particularly well suited for studies on cell differentiation and effects of pharmacological and other experimental treatments on cell fine structure. It represents an alternative and a complement to stereology for quantitative and objective evaluation of morphological data.

The key programming language used in the field of data science is R programming, because of the freeavailability and ability to handle huge data. Packages developed in the R are used widely by scientists toobtain solutions for various real-world problems in several disciplines like healthcare, agriculture, andinformation technology. Next-generation sequencing data requires various bioinformatics analyses likequality checking, differential gene expression studies, and annotation which is facilitated by R packages andsoftware. Bioconductorprojectremains a hub of R packages that are open access and move the researchers tothe comfort zone for various kinds of analysis. In this review, we briefly discussed various packages usefulfor NGS data analysis and also explained how to use the packages for basic level analysis that benefitsresearchers having less exposure to R programming.

A quantum mechanical calculation of the vibrational levels of the HgAr2([graphic omitted]+) Van der Waals cluster has been presented and a statistical analysis of the level distribution has been conducted. The theoretical methods are those used by Leitner et al.(J. Chem. Phys., 1981, 91, 3470) for a study of quantum chaos in the Ar3 cluster. The potential-energy surface is obtained from semiempirical Ar⋯Ar and Ar⋯Hg(3P1) interactions using appropriate axis switching rotation and electronically adiabatic diagonalization. The vibrational energy levels are calculated by successive diagonalizations and truncations using DVR basis sets in Radau coordinates. The probability distribution of level spacings and the fluctuations of the level positions have been studied and compared with Poisson and Wigner distributions. As for the Ar3 case studied by Leitner et al., the statistics resemble the Wigner distribution expected for chaotic dynamics and there is very little evidence for regular or intermediate behaviour.

Integration of renewable distributed generation technology with radial power distribution system is rapidly growing. Among the number of available renewable energy sources, the role of wind energy in the power sector is very important. In this work, authors have estimated the wind energy potential at Banaras Hindu University (BHU), India. Estimation of wind energy potential depends on statistical analysis of wind speed distribution, which will give us the best-fitted probability density function of the desired location. For statistical analysis of wind speed distribution, authors have taken hourly data of BHU centre from the source of National Renewable Energy Laboratory (NREL), USA for the 12-month period. A statistical R-programming language tool has been used for the computational work. In this work, authors have considered Weibull, Gamma and Lognormal probability distributions for getting best-fitted distribution. After the analysis, result shows for the given wind speed data of BHU area, Weibull distribution is the best-fitted one.