Enter the number of trials, number of successes, and probability of success on trial into the calculator to determine the negative binomial.

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## Negative Binomial Formula

The following formula can be used to calculate the negative binomial of distribution.

P = k*(1-p)/p

- Where P is the negative binomial
- p is the probability of success
- k is the number of success

## Negative Binomial Definition

The Negative Binomial is a probability distribution that models the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified number of failures occur. It is characterized by two parameters: the number of failures required, denoted as r, and the probability of success in a single trial, denoted as p.

To understand the Negative Binomial, let’s consider an example. Suppose we are flipping a biased coin where the probability of getting a head is p. We are interested in knowing how many times we need to flip the coin until we get r tails. The Negative Binomial distribution allows us to calculate the probability of getting a specific number of successes (heads) before observing r failures (tails).

The Negative Binomial is important in various fields, including statistics, economics, and biology, because it provides a flexible and useful model for situations where we are interested in the number of trials needed to achieve a certain number of failures. It allows us to analyze data that exhibits overdispersion, meaning the variance is higher than what would be expected under a simpler distribution like the Binomial or Poisson.

## Negative Binomial Example

How to calculate a negative binomial?

**First, determine the number of successes.**Measure the total number of successes.

**Next, determine the total probability of success.**Calculate the probability of success.

**Finally, calculate the negative binomial.**Calculate the negative binomial using the formula above.

## FAQ

**What is a negative binomial?**

Also known as pascal distribution, a negative binomial distribution is a probability solution that models the number of successes in a sequence of Bernoulli trials.