Abstract
The binomial (Bernoulli), multinomial, negative binomial (Pascal), and Poisson distributions are presented as the most frequently occurring discrete probability distributions in practice. The normal approximation of the binomial distribution is introduced as an example of the Laplace limit theorem, and the Poisson distribution is shown to represent a special limiting case of the binomial.
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Notes
- 1.
The ‘negative’ attribute in the name of the distribution originates in the property
$$ \left( {n+r-1\atop n} \right) = (-1)^n \frac{(-r)(-r-1)(-r-2) \ldots (-r-n+1)}{n!} = (-1)^n \left( {-r \atop n} \right) . $$.
References
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F. Sauli, Principles of Operation of Multiwire Proportional and Drift Chambers (CERN Reprint 77–09, Geneva, 1977)
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Širca, S. (2016). Special Discrete Probability Distributions. In: Probability for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31611-6_5
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DOI: https://doi.org/10.1007/978-3-319-31611-6_5
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