The Tail Distribution of the Sum of Kappa Random Variables with Unequal Weight and Correlation

Applications of the Kappa distribution, which is used to describe the particle velocity distribution when a system is in thermal anti-equilibrium, to statistical mechanics and high frequency (HF) communication are considered. In particular, the tail distribution of the sum of Kappa random variables (RVs) is studied. First, an approximation for the sum of unequally weighted, uncorrelated Kappa RVs is found that provides results for the tail distribution of that sum. Correlated Kappa RVs are then examined by using the Cholesky decomposition to obtain similar results. Simulation results are shown to agree with this development.