Implementation of Multivariate Exponential Power Distribution in Discrimination and Classification of Psychological Data and Other applications

Recent advances have shown that some multivariate psychological data are deviating from usual normal assumption either in the tails or kurtosis. Thereby, allowing the call for modelling of such data using more robust elliptically contoured density which includes the normal distribution as a special case. This allowed more flexibility at the kurtosis and tail regions, which is better in handling non-normality in data analysis and also lower the cost of misclassification. The present study employed a robust model for such cases in the context of discrimination and classification of multivariate psychological disorder data using multivariate exponential distribution as an underlining model. Parameters were estimated using the method of maximum likelihood estimation and the discrimination and classification were based on the log likelihood ratio approach. The resulting models relied solidly on the shape parameter, which regulate the tails and the kurtosis, thereby allowed flexibility. This method enable us to lower the cost of misclassification. Some other areas of applications were also considered in the paper.

Distribution-Based Entropy Weighting Clustering of Skewed and Heavy Tailed Time Series

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties, such as heavy tails and skewness. Thanks to its flexibility, the skewed exponential power distribution (also called skewed generalized error distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is shown by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.

Generalized Exponential Power Distribution with Application to Complete and Censored Data

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

Distribution-Based Entropy Weighting Clustering of Skewed Time Series

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series have motivated the development of classes of distributions that can accommodate properties such as heavy tails and skewness. Thanks to its flexibility, the Skew Exponential Power Distribution (also called Skew Generalized Error Distribution) ensures a unified and general framework for clustering possibly skewed time series. This paper develop a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine all the parameter estimates to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is showed by means of an application to financial time series, showing also how the obtained clusters can be used to form portfolio of stocks.

Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method

This paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy

Log-Exponential Power Distribution for Accelerated Failure Time Model in Survival Analysis and Its Application

We proposed the log-exponential power density function as baseline distribution for accelerated failure time model (AFT) used in analysis of survival data with covariates. This model generalizes the log-normal and some exponential family due to flexibility at the tail region. It has log-concavity property, accommodates the four basic shapes of hazard function which is an attractive property compared with other distributions that cannot accommodate same. The model's goodness of fit relative to some existing models was tested using data from chronic liver disease patients monitored at Obafemi Awolowo University Teaching Hospital, Ile-Ife