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

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?

  1. First, determine the number of successes.

    Measure the total number of successes.

  2. Next, determine the total probability of success.

    Calculate the probability of success.

  3. Finally, calculate the negative binomial.

    Calculate the negative binomial using the formula above.


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.

negative binomial calculator
negative binomial formula