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.
Distribution name

Negative
binomial distribution

Common notation


Parameters

=
number of failures ()
=
probability of success in each experiment ()

Support


Probability mass
function

If is nonintegral
then is:

Cumulative distribution
function


Mean


Variance


Skewness


(Excess) kurtosis


Characteristic function


Other comments

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:

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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