On a Generalized Entropy Measure Leading to the Pathway Model: with a preliminary application to solar neutrino data

An entropy for the scalar variable case, parallel to Havrda-Charvat entropy was introduced by the first author and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper we extend the entropy to cover scalar case, multivariable case, and matrix variate case. Then this measure is optimized under different types of restrictions and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical, physical, and engineering sciences are also pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data is provided.