Negative binomial inverse cumulative distribution function
X = nbininv(Y,R,P)
X = nbininv(Y,R,P) returns
the inverse of the negative binomial cdf with corresponding number
R and probability of success in a
P. Since the binomial distribution
nbininv returns the least integer
that the negative binomial cdf evaluated at
P can be vectors, matrices, or multidimensional
arrays that all have the same size, which is also the size of
A scalar input for
expanded to a constant array with the same dimensions as the other
The simplest motivation for the negative binomial is the case
of successive random trials, each having a constant probability
success. The number of extra trials you must
perform in order to observe a given number
successes has a negative binomial distribution. However, consistent
with a more general interpretation of the negative binomial,
be any positive value, including nonintegers.
How many times would you need to flip a fair coin to have a 99% probability of having observed 10 heads?
flips = nbininv(0.99,10,0.5) + 10 flips = 33
Note that you have to flip at least 10 times to get 10 heads. That is why the second term on the right side of the equals sign is a 10.