A Closed-Form Approximation for the CDF of the Sum of Independent Random Variables

In this letter, we use the Berry–Esseen theorem and the method of tilted distributions to derive a simple tight closed-form approximation for the tail probabilities of a sum of independent but not necessarily identically distributed random variables. We also provide lower and upper bounds. The expression can also be used for computing the cumulative distribution function. We illustrate the accuracy of the method by analyzing some convergence properties of the theoretical approximation and comparing it with previous results in the literature when available and/or numerical results.

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