Journal of Computational Engineering / 2015 / Article / Fig 13

Research Article

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

Figure 13

histogram: cross markers (black color), numerical simulation; circle markers (red color), analytical solution. The PDF of is a chi square distribution with two degrees of freedom, which is shifted by 1000 unit, and the one of is a uniform distribution. and are 1000 and 1645, 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 ; ; ; . 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. ; ; .

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