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--- negative_binomial_distribution [2023/03/10 11:56]
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-====== Negative binomial Distribution ======
-In probability and statistics the negative binomial distribution is a discrete probability distribution. The Pascal distribution and the Polya distribution are special cases of the negative binomial. There is a convention among engineers, climatologists, and others to reserve “negative binomial” in a strict sense or “Pascal” (after Blaise Pascal) for the case of an integer-valued parameter r, and use “Polya” (for George Pólya) for the real-valued case, to the right. The Polya distribution more accurately models occurrences of “contagious” discrete events, like tornado outbreaks, than does the Poisson distribution.
-The family of negative binomial distributions is a two-parameter family; several parametrizations are in common use. One very common parameterization employs two real-valued parameters p and r with 0 p 1 and r > 0. Under this parameterization, the probability mass function of a random variable with a NegBin(r, p) distribution takes the following form:
-f(x,r,p) = (x+r-1) “over” (x) * p^r//(1-p)^x//
-support x = 0,1,2,3,…
-^Parameter^Description^Default value^
-|r        |           |5.0          |
-|p        |           |0.5          |

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