Generalized ‘Useful’ Rényi & Tsallis Information Measures, Some Discussions with Application to Rainfall Data

Abstract

In this manuscript ‘useful’ Renyi and ‘useful’ Tsallis information measures and respective divergence measures are defined. It has been proved with the help of rule of differentiability that ‘useful’ Renyi and ‘useful’ Tsallis information measures reduce to Shannon's information measure, while ‘useful’ Renyi and ‘useful’ Tsallis information divergence measure reduce to Kullback-Leibler divergence measure as parameter α→1.Further rainfall data for region in district Guna in Madhya Pradesh, India for years 2013-2018 has been analyzed using ‘useful’ Renyi and ‘useful’ Tsallis information measures with an aim to assist farmers in the region with planning agricultural activities like seeding, cultivating and harvesting.