An Estimate of the Probability Density Function of the Sum of a Random Number N of Independent Random Variables

A new estimate of the probability density function (PDF) of the sum of a random number of independent and identically distributed (IID) random variables Xi (i=1, 2, …, N) is shown. The sum PDF is represented as a sum of normal PDFs weighted according to the N PDF. The analytical model is verified by numerical simulations. The comparison is made by the Chi-Square Goodness-of-Fit test