The authors recently derived a method for assessing stochastic randomness in three dimensional Euclidean space. The method was derived from a nearest neighbor spatial Poisson process. An alternative probability model based on a box-counting method derived from a partial sum of a Poisson series is presented in this paper. The performance of the method is evaluated through Monte Carlo simulations with synthetically constructed random distributions. A comparison between the new discrete distribution method and the initial distance method showed that a greater likelihood of detecting randomness existed among populations with the box-counting method.
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References
1.
FellerW. (1950) An introduction to probability theory and its applications. Vols. 1, 2. New York: Wiley.
2.
O'BrienF. (1994a) Probability methods for detecting randomness in small sample spatial distributions. Perceptual and Motor Skills, 78, 715–720.
3.
O'BrienF. (1994b) A test of randomness for finite spatial distributions. Perceptual and Motor Skills, 78, 707–714.
4.
O'BrienF. (1995) Comparison of two tests of planar randomness. Perceptual and Motor Skills, 80, 144–146.
5.
O'BrienF.HammelS. E.NguyenC. T. (1995) A test for randomness in three dimensions. Perceptual and Motor Skills, 81, 115–119.
