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In probability theory and statistics, the index of dispersion, dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard statistical model.
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphazardness; it is a measure of uncertainty of an outcome. Randomness applies to concepts of chance, probability, and information entropy.
In probability theory, statistics and related fields, a Poisson point process is a type of mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The process's name derives from the fact that the distribution of the number of points regions of the same size has a Poisson distribution. The process and the distribution are named after French mathematician Siméon Denis Poisson. The process itself was discovered independently and repeatedly in several settings, including experiments on radioactive decay, telephone call arrivals and actuarial science.
References
- ↑ A. Kolmogorov, "Foundations of the theory of probability" 1933. English translation by Nathan Morrison 1956 copyright Chelsea Publishing Company.
- ↑ R. Christensen and T. Reichert: "Unit measure violations in pattern recognition: ambiguity and irrelevancy" Pattern Recognition, 8, No. 4 1976.
- ↑ T. Oldberg and R. Christensen "Erratic measure" NDE for the Energy Industry 1995, American Society of Mechanical Engineers, New York, NY.