Negative Binomial Calculator

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

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