Discrete inaccuracy information measure: extension and application to image processing

OpenAlex İngilizce

This paper extends the concepts of inaccuracy information and varinaccuracy to the discrete domain, examining their connections with Shannon entropy, Burg entropy, Rényi entropy, Kullback-Leibler divergence, and discrete information generating measures. We examine the discrete inaccuracy information measure for escort and generalized escort probability mass functions, which are well-known models in coding theory and non-extensive thermodynamics. We also introduce the discrete fractional inaccuracy, Jensen-discrete inaccuracy, discrete variance-based inaccuracy, and Jensen-discrete variance-based inaccuracy measures, exploring their properties. Furthermore, a new relative-discrete fractional inaccuracy measure is proposed, encompassing the Jensen-discrete inaccuracy as a special case. Finally, we demonstrate the utility of the proposed discrete fractional inaccuracy measure through an image processing example and hypothesis tests for Poisson distribution, showcasing its effectiveness in assessing similarity, divergence, and model fit.