An alternative multivariate exponential power distribution

Abstract

In the existing multivariate Exponential Power Distribution (MEPD), the shape parameter has the tendency to affect the variability in the data leading to distorted features of the distribution. “This study resolves this problem by obtaining a generalized expression in place of the constant coefficient (0.5) of the quadratic form of the Multivariate EPD as a function of the shape parameter, such that the variance-covariance matrix of the data is exactly equal to the scale parameter. The alternative Multivariate EPD (AMEPD) thus obtained is a more generalized multivariate EPD. The maximum likelihood estimation (MLE) of the parameters of the distribution are presented via Newton-Ralphson method. The estimates based on the proposed distribution is compared to other methods using information criteria.” Results consistently indicate superior performance of the AMEPD to the MEPD for various sample sizes based on both simulated and empirical datasets. The study further explores the application of the new distribution in discriminant analysis under the assumptions of equal and unequal variance-covariance matrices. The application also underscores the importance of accurate specification of the variance-covariance matrix for the desired predictive performance. The proposed approach has the potential to provide a more robust statistical model for complex multivariate distributions that are close to symmetry as it provides greater flexibility in depicting the true underlying characteristics of the distributions.