# Manuals/calci/NEGBINOMDIST

**NEGBINOMDIST(x,r,p)**

- is the number of failures.
- is the number of successes on an individual trial
- is the probability of a success.
- NEGBINOMDIST(), returns the negative binomial distribution.

## Description

- This function gives the Negative Binomial Distribution.
- Negative Binomial Distribution is the discrete probability distribution with the fixed probability of success.
- It is also called Pascal Distribution.

This is the statistical experiment with the following conditions:

This experiment consists of a sequence of independent trials. Each trial represents only two results(Success or failure) The probability of success is constant from trial to trial The trials are independent; ie, the outcome on one trial does not affect the outcome on other trials. The experiment continues until the successes is obtained, where is a specified positive integer.

- The random variable = the number of failures that precede the success;
- is called a Negative Binomial Random variable because, in contrast to the

binomial random variable, the number of successes is fixed and the number of trials is random.

- Then probability mass function of the negative binomial distribution is

- For example: If a fair coin is tossed repeatedly, what is the probability that at least 10 tosses are required.

to obtain heads 8 times

- This function will give the result as error when:

- Any argument is non-numeric
- If or
- If or

## ZOS

- The syntax is to calculate NEGBINOMDIST in ZOS is .
- where is the number of failures.
- is the number of successes on an individual trial
- is the probability of a success.

- For e.g.,NEGBINOMDIST(8..9,5..7,0.5).

## Examples

- Find the probability that a man flipping a coin gets the fourth head on the ninth flip.

Here total number of events =9, r= 4(since we define Heads as a success) and x=9-4=5(number of failures)

p=1/2=0.5(Probability of success for any coin flip)

NEGBINOMDIST(5,4,0.5)=0.109375

- A company conducts a geological study that indicates that an exploratory goods well should have a 20% chance of striking goods. What is the probability that the first strike comes on the third well drilled?

Here total number of events=3, r=1,x=3-1=2,and p=0.20 NEGBINOMDIST(2,1,0.20)=0.128

- What is the probability that the fourth strike comes on the eighth well drilled?

Here total number of events=8, r=4, x=8-4=4 and p=0.20 NEGBINOMDIST(4,4,0.20)=0.0229376

## Related Videos

## See Also

## References