ight Exact Expressions for the Sum of Weibull Random Variable

Sums of Weibull variates arise in several communications fields, such as optical, mobile, and radar systems. However, due to the intricate task of evaluating the Weibull sums, only a few works deal with the exact sum statistics. Some of these works provide solutions in terms of nested infinite sums-products, approximate solutions, or in terms of especial functions that, unfortunately, have not yet been implemented in mathematical packages such as Maple, MATLAB, or Mathematica. Yet, these solutions are time-consuming and prone to convergence and instability problems as the number of Weibull summands increases. In this letter, based on a comprehensive calculus of residues, we derive novel exact expressions for the probability density function and the cumulative distribution function of the sum of independent and identically distributed Weibull random variables. Numerical results show that our derived solutions are faster and enjoy a lower computational burden than the state-of-the-art ones. (AU)