Manuals/calci/NEGBINOMDIST

NEGBINOMDIST(x,r,p)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is the number of failures.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the number of successes on an individual trial
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} is the probability of a success.

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r}
 the successes is obtained, where   is a specified positive integer.

The random variable Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} = the number of failures that precede the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r^{th}} success;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle nb(x;r,p)=(x+r-1 p^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:

Any argument is non-numeric
If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ps<0} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ps>1}
If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle nf<0} or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ns<1}

ZOS

The syntax is to calculate NEGBINOMDIST in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NEGBINOMDIST(x,r,p)} .
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is the number of failures.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the number of successes on an individual trial
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} is the probability of a success.
For e.g.,NEGBINOMDIST(8..9,5..7,0.5).

Negative Binomial Distribution

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