Supervised Classification Using Finite Mixture Copula

Use of copula for statistical classification is recent and gaining popularity. For example, statistical classification using copula has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rules assume normality. But in this data age time, this assumption is often questionable. In fact features of data could be a mixture of discrete and continues random variables. In this paper, mixture copula densities are used to model class conditional distributions. Such types of densities are useful when the marginal densities of the vector of features are not normally distributed and are of a mixed kind of variables. Authors have shown that such mixture models are very useful for uncovering hidden structures in the data, and used them for clustering in data mining. Under such mixture models, maximum likelihood estimation methods are not suitable and regular expectation maximization algorithm is inefficient and may not converge. A new estimation method is proposed to estimate such densities and build the classifier based on mixture finite Gaussian densities. Simulations are used to compare the performance of the copula based classifier with classical normal distribution based models, logistic regression based model and independent model cases. The method is also applied to a real data

Copula-Based Models for Bivariate and Multivariate Zero-inflated Count Time Series Data

Count time series data have multiple applications. The applications can be found in areas of finance, climate, public health and crime data analyses. In some scenarios, count time series come as multivariate vectors that exhibit not only serial dependence within each time series but also with cross correlation among the series. When considering these observed counts, analysis presents crucial challenges when a value, say zero, occurs more often than usual. There is presence of zero-inflation in the data. In this presentation, we mainly focus on modeling bivariate zero-inflated count time series model based on a joint distribution of the two consecutive observations. The bivariate zero-inflated models are constructed through copula functions. Such Gaussian copula can accommodate both serial dependence and cross-sectional dependence in zero-inflated count time series data. We consider the first order Markov chains with zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB) and zero-inflated Conway-Maxwell-Poisson (ZICMP) marginals. Bivariate copula functions such as the bivariate Gaussian and t-copula are chosen to construct the distribution of consecutive observations. Likelihood based inference is used to estimate the model parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized importance sampling method. To evaluate the superiority of the model, simulated (under positive and negative cross-correlations) are provided and presented. Real data examples are also shared. Extensions for high dimensional scenarios are discussed by introducing the copula autoregressive model (COPAR) with pair copula construction and vine tree structure. Structure matrices of the COPAR of orders 1 and 2 are shown. Simulations are conducted to validate the models.https://digitalcommons.odu.edu/gradposters2023_sciences/1026/thumbnail.jp

The Joint Distribution of Bivariate Exponential Under Linearly Related Model

In this paper, fundamental results of the joint distribution of the bivariate exponential distributions are established. The positive support multivariate distribution theory is important in reliability and survival analysis, and we applied it to the case where more than one failure or survival is observed in a given study. Usually, the multivariate distribution is restricted to those with marginal distributions of a specified and familiar lifetime family. The family of exponential distribution contains the absolutely continuous and discrete case models with a nonzero probability on a set of measure zero. Examples are given, and estimators are developed and applied to simulated data. Our findings generalize substantially known results in the literature, provide flexible and novel approach for modeling related events that can occur simultaneously from one based event

Linear Dependency for the Difference in Exponential Regression

In the field of reliability, a lot has been written on the analysis of phenomena that are related. Estimation of the difference of two population means have been mostly formulated under the no-correlation assumption. However, in many situations, there is a correlation involved. This paper addresses this issue. A sequential estimation method for linearly related lifetime distributions is presented. Estimations for the scale parameters of the exponential distribution are given under square error loss using a sequential prediction method. Optimal stopping rules are discussed using concepts of mean criteria, and numerical results are presented

On Weighted Distributions and Mean Advantage Over Inferiors Functions

In this note, some fundamental results including relationship be-tween weighted distribution functions and mean advantage over inferi-ors functions are established. Ordering of reliability and/or distribution functions via mean advantage over inferiors functions and related func-tions for parent and weighted reliability functions are presented. Some applications and examples are given

Therapeutic Breathing Techniques and Disparity Across Student Performance in English and Mathematics

This paper explores possible correlation between Therapeutic Breathing Techniques (TBT) and improved academic performance of low achieving students in elementary school. The intervention consisted of daily breathing exercises combining two forms of TBT, namely, deep breathing and alternate nostril breathing. A semester-long quantitative study with 85 second graders was conducted to investigate the impact of above intervention on English and mathematics scores. Following one semester of intervention, the gaps between the low and high achievers had narrowed and small but significant gain-scores were found for the low achievers who had practiced TBT. In contrast, in first and third grades, where neither low achievers nor high achievers received the treatment, the gap between the low and high achievers widened slightly. The findings indicate the need to further investigate the potential merit of therapeutic breathing exercises as a low-cost intervention strategy for improving school performance and addressing achievement gaps, especially in mathematics

Physical Activity, Dietary Patterns, and Glycemic Management of Active Individuals with Type 1 Diabetes: An Online Survey

Individuals with type 1 diabetes (T1D) are able to balance their blood glucose levels while engaging in a wide variety of physical activities and sports. However, insulin use forces them to contend with many daily training and performance challenges involved with fine-tuning medication dosing, physical activity levels, and dietary patterns to optimize their participation and performance. The aim of this study was to ascertain which variables related to the diabetes management of physically active individuals with T1D have the greatest impact on overall blood glucose levels (reported as A1C) in a real-world setting. A total of 220 individuals with T1D completed an online survey to self-report information about their glycemic management, physical activity patterns, carbohydrate and dietary intake, use of diabetes technologies, and other variables that impact diabetes management and health. In analyzing many variables affecting glycemic management, the primary significant finding was that A1C values in lower, recommended ranges

A Bivariate Distribution with Conditional Gamma and its Multivariate Form

A bivariate distribution whose marginal are gamma and beta prime distribution is introduced. The distribution is derived and the generation of such bivariate sample is shown. Extension of the results are given in the multivariate case under a joint independent component analysis method. Simulated applications are given and they show consistency of our approach. Estimation procedures for the bivariate case are provided

Dynamic Attribute-Level Best Worst Discrete Choice Experiments

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are computationally consistent with decision choices over time

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models