nbinstat
Negative binomial mean and variance
Syntax
[M,V] = nbinstat(R,P)
Description
[M,V] = nbinstat(R,P)
returns
the mean of and variance for the negative binomial distribution with
corresponding number of successes, R
and probability
of success in a single trial, P
. R
and P
can
be vectors, matrices, or multidimensional arrays that all have the
same size, which is also the size of M
and V
.
A scalar input for R
or P
is
expanded to a constant array with the same dimensions as the other
input.
The mean of the negative binomial distribution with parameters r and p is rq / p, where q = 1 – p. The variance is rq / p2.
The simplest motivation for the negative binomial is the case
of successive random trials, each having a constant probability P
of
success. The number of extra trials you must
perform in order to observe a given number R
of
successes has a negative binomial distribution. However, consistent
with a more general interpretation of the negative binomial, nbinstat
allows R
to
be any positive value, including nonintegers.
Examples
p = 0.1:0.2:0.9; r = 1:5; [R,P] = meshgrid(r,p); [M,V] = nbinstat(R,P) M = 9.0000 18.0000 27.0000 36.0000 45.0000 2.3333 4.6667 7.0000 9.3333 11.6667 1.0000 2.0000 3.0000 4.0000 5.0000 0.4286 0.8571 1.2857 1.7143 2.1429 0.1111 0.2222 0.3333 0.4444 0.5556 V = 90.0000 180.0000 270.0000 360.0000 450.0000 7.7778 15.5556 23.3333 31.1111 38.8889 2.0000 4.0000 6.0000 8.0000 10.0000 0.6122 1.2245 1.8367 2.4490 3.0612 0.1235 0.2469 0.3704 0.4938 0.6173
Extended Capabilities
Version History
Introduced before R2006a