The negative binomial distribution
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The negative binomial distribution describes the probability
of 
successes in a
sequence of independent experiments each with likelihood of success of 
that
arise before there are 
failures. In this
interpretation is a positive
integer, but the distributional definition can also be extended to real values
of 
. Note: different
texts adopt slightly different definitions, e.g. with support starting at 
not
and/or with denoting
probability of failure rather than probability of success.
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Distribution name
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Negative
binomial distribution
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Common notation
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Parameters
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=
number of failures ()
=
probability of success in each experiment ( )
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Support
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Probability mass
function
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If is non-integral
then is:
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Cumulative distribution
function
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Mean
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Variance
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Skewness
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(Excess) kurtosis
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Characteristic function
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Other comments
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The geometric distribution is the same as the
negative binomial distribution with parameter  .
Its pdf and cdf are therefore:
For the special case where is
an integer the negative binomial distribution is also called the Pascal
distribution. The Poisson
distribution is also a limiting case of the negative binomial:
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Nematrian web functions
Functions relating to the above distribution may be accessed
via the Nematrian
web function library by using a DistributionName of “negative
binomial”. For details of other supported probability distributions see here.
NAVIGATION LINKS
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