# 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.

• This function will give the result as error when:
1. Any argument is non-numeric
2. If or
3. 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).
Negative Binomial Distribution

## Examples

1. 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

1. 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

1. 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

Negative Binomial Distribution