The probability density function of an area covered with disks whose centers are randomly distributed

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Abstract
Using Monte Carlo simulation, this paper examines the probability density function, f(s), of an area, s, covered with disks whose centers are randomly distributed over a square region. First, an efficient computational method for calculating s is shown. Second, by the use of this method, s is calculated 5,000 times, and the mean, variance, skewness and kurtosis of f(s) are obtained. These results indicate that f(s) is skewed and cannot be regarded as the normal distribution for a certain range of parameter values. Last, for the use of a statistical test in applications, critical values of f(s) of significance levels .025 and .050 are obtained from the simulation data and tabulated with respect to the number of disks, 10, 25, 50, 100, and the radius of a disk.

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