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

JUAN AUGUSTO MAYA; LEONARDO REY VEGA; CECILIA GABRIELA GALARZA

IEEE SIGNAL PROCESSING LETTERS

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

Lugar: New York; Año: 2017 vol. 24 p. 121 - 125

1070-9908

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 availableand/or numerical results.