The negative binomial distribution, especially in its alternative parameterization described above, can be used as an alternative to the Poisson distribution.
12.
The series of ball passing between players during football matches was successfully analyzed using negative binomial distribution by Reep and Benjamin in 1968.
13.
This property persists when the definition is thus generalized, and affords a quick way to see that the negative binomial distribution is infinitely divisible.
14.
Also notice that the marginal is simply the integral of the posterior over all \ Theta, which turns out to be a negative binomial distribution.
15.
The negative binomial distribution is also commonly used to model gene expression in the form of discrete read count data from high-throughput RNA sequencing experiments.
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Other special cases include : shiftgeometric distribution, negative binomial distribution, Geometric Poisson distribution, Neyman type A distribution, Luria Delbr�ck distribution in Luria Delbr�ck experiment.
17.
For the special case where " r " is an integer, the negative binomial distribution is known as the "'Pascal distribution " '.
18.
Then M is the number of successes before ( N + 1 ) failures in Bernoulli trials with p = 1 / 2, which has the negative binomial distribution and thus
19.
Well-known discrete probability distributions used in statistical modeling include the Poisson distribution, the Bernoulli distribution, the binomial distribution, the geometric distribution, and the negative binomial distribution.
20.
The geometric distribution, for the number of failures before the first success, is a special case of the negative binomial distribution, for the number of failures before s successes.
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