# NEGBINOM.DIST Function in Excel

NEGBINOM.DIST Function in Excel calculates the Negative Binomial Distribution for a given set of parameters.it returns either probability mass function or the cumulative distribution function depending on input. Negative binomial distribution gives the probability that there will be a specified number of failures before a required number of successes is achieved.

Negative Binomial Distribution Formula:Negative Binomial Distribution Formula for rth success occurring on xth trial is shown below Where,

x: is the number of trials
r: The required number of successes.
p: The probability of success on an individual trial.
q: The probability of failure on an individual trial (q= 1-p)

Syntax of NEGBINOM.DIST Function in Excel:

NEGBINOM.DIST( number_f, number_s, probability_s, cumulative)

Where,

number_f – The number of Failures encountered before the number of success.

number_s  –  The number of successes

probability_s– The probability of success(for a single trial).

cumulative – A logical argument, if TRUE returns the cumulative distribution function.If FALSE returns the probability mass function.

#### Example of NEGBINOM.DIST Function in Excel which uses probability mass function:

Let’s take an Example of Negative Binomial Distribution Function for the probability that the toss of a coin will result in exactly X Heads before 5 tossed Tails.

##### Formula: • If NEGBINOM.DIST Function takes up FALSE argument then it results in probability mass function
##### Result: When we plot the above result with number of failures before the success on x axis. We will get the probability mass function graph.

#### Example of NEGBINOM.DIST Function in Excel which uses cumulative distribution function:

##### Formula • If NEGBINOM.DIST Function takes up TRUE argument then it results in cumulative distribution function
##### Result When we plot the above result with number of failures before the success on x axis. We will get the cumulative distribution function graph. 