The NEGBINOM.DIST function in Excel is designed to calculate the probability of a specific number of successes in a negative binomial distribution scenario. This statistical function is particularly relevant in situations where we are interested in the count of failures before achieving a predetermined number of successes. By employing this function, users can efficiently derive probabilities used in various applications, such as quality control and reliability testing.

Syntax

NEGBINOM.DIST(successes, failures, probability_s, cumulative)

• successes: The number of successful trials you want to achieve.
• failures: The number of failed trials that occur before the desired successes.
• probability_s: The probability of success on an individual trial.
• cumulative: A logical value that determines the form of the function. If TRUE, it calculates the cumulative distribution function; if FALSE, it calculates the probability mass function.

Example #1

=NEGBINOM.DIST(5, 2, 0.3, FALSE)

This function calculates the probability of having exactly 2 failures before achieving 5 successes when the probability of success in each trial is 30%. The result of this function would be approximately 0.183.

Example #2

=NEGBINOM.DIST(3, 4, 0.5, TRUE)

This example computes the cumulative probability of getting up to 4 failures before attaining 3 successful trials, each having a success probability of 50%. The result yields about 0.843.

Example #3

=NEGBINOM.DIST(1, 5, 0.2, FALSE)

This function determines the probability of having exactly 5 failures before achieving the first success, with a success rate of 20%. The output value would be around 0.026.

Error handling

• VALUE! One or more arguments are of the incorrect type, such as text instead of numbers.
• NUM! At least one argument is outside the allowed range. For example, negative values or probabilities greater than 1.
• N/A! The function cannot calculate a result due to mathematical constraints, such as non-integer values for the successes or failures.

Conclusion

The NEGBINOM.DIST function is a useful tool for performing calculations related to negative binomial distributions in Excel. By understanding its syntax and application, users can derive essential probabilities that aid in statistical modeling and analysis. Leveraging this function can significantly enhance decision-making processes in various fields, including finance, healthcare, and quality assurance.