67 – Section on Statistical Computing: Data Science
Positive Orthant Hyperspherical Distribution and Applications
Jose H. Guardiola
Texas A&M University-Corpus Christi
In text mining, gene expressions and machine learning there is a need to model vectors at the positive orthant of the hypersphere. Similarly, in compositional data analysis a square root transformation can also be used to map the simplex onto the mentioned subspace. This paper focuses in developing a probability distribution on that region avoiding unnecessary probability mass at the whole hypersphere. We modified a proposed spherical Dirichlet distribution proposing a flexible version of this distribution. The distribution basic properties, such as normalizing constants and moments are developed. Efficient estimators based on classical inferential statistics are also obtained. An application using simulated data and a text mining example are developed and their results are discussed.