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  • 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.


  • 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:
  1. Any argument is non-numeric
  2. If or
  3. If or


  • 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


  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)


  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

See Also