Manuals/calci/NEGBINOMDIST

NEGBINOMDIST(x,r,p)

• $x$ is the number of failures.
• $r$ is the number of successes on an individual trial
• $p$ 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 $r$ the successes is obtained, where $r$ is a specified positive integer. 

• The random variable $x$ = the number of failures that precede the $r^{th}$ success;
• $x$ 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

$nb(x;r,p)=(x+r-1p^{r}(1-p)^{x}r-1)$

• 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 $ps<0$ or $ps>1$
3. If $nf<0$ or $ns<1$

ZOS

• The syntax is to calculate NEGBINOMDIST in ZOS is $NEGBINOMDIST(x,r,p)$.
  • where $x$ is the number of failures.
  • $r$ is the number of successes on an individual trial
  • $p$ 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

See Also

• LN
• IMLOG10
• LOG

References

Logarithm

• List of Main Z Functions

• Z3 home