# cdfNegBinomial¶

## Purpose¶

Computes the cumulative distribution function for the negative binomial distribution.

## Format¶

p = cdfNegBinomial(f, s, prob)
Parameters: f (NxK matrix, Nx1 vector or scalar) – Number of failures. $$0 < f$$. s (matrix) – ExE conformable with f, the number of successes. $$0 < s$$. prob (matrix) – The probability of success on any given trial. ExE conformable with f. $$0 < prob < 1$$. p (NxK matrix, Nx1 vector or scalar) – The probability of observing f failures before observing s successes.

## Remarks¶

For invalid inputs, cdfNegBinomial() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr will return a 1; if the second is out of range, scalerr() will return a 2; etc.

## Example¶

Pat has to sell five candy bars to raise money for the 6th grade field trip. So the child goes door to door, selling candy bars. At each house, there is a 0.4 probability of selling one candy bar and a 0.6 probability of selling nothing.

What’s the probability that Pat finishes on or before reaching houses five through eight?

// f is number of failures, f = 0, 1, 2, 3
f = seqa(0, 1, 4);

// Probability of selling each candy bar is 0.4
prob = 0.4;

// Number of successes (sold candy bars)
s = 5;

p = cdfNegBinomial(f, s, prob);

// 5 successes + f failures = total houses visited
h = f + 5;

print  "After nth try, the probability =";
print h~p;


After running above code, the probability that Pat finishes on or before reaching the eighth house is 0.1736704 or 17.36704%. The other probabilities are also listed below.

After nth try, the probability =

5.0000000      0.010240000
6.0000000      0.040960000
7.0000000      0.096256000
8.0000000       0.17367040