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

Figure 10

histogram: cross markers (black color), numerical simulation; circle markers (red color), analytical solution. The PDFs of and are both uniform distributions. and are 2292 and 57703, respectively. The null hypothesis is a uniform PDF with mean and variance given by (3) and (4), respectively. The means and standard deviations of and are ; ; ; . The sample number is 10000 and the number of bins is 60. The chi squared test is accepted at the significance level of 0.05. ; ; .