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

Figure 11

histogram: cross markers (black color), numerical simulation; circle markers (red color), analytical solution. The PDFs of and are both uniform distributions. and are 97 and 103, respectively. The null hypothesis is the PDF of the simulated data with mean and variance given by (3) and (4), respectively. The means and standard deviations of and are ; ; ; . In this case, the sample number is 100000 and the number of bins is 1000. The chi squared test is accepted at the significance level of 0.05. ; ; .