Negative Binomial Distribution Calculator

Analyze data using the negative binomial distribution with our calculator.


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The Negative Binomial Distribution Calculator helps you determine probabilities in a specific type of discrete probability distribution. The negative binomial distribution models the number of trials needed until a specified number of successes occur, where each trial has two possible outcomes: success or failure.

Using the Calculator

Follow these steps to calculate probabilities using the Negative Binomial Distribution:

  1. Enter the number of events (n) – the number of trials to reach the specified number of successes. It must be a non-negative integer.
  2. Enter the number of successes (r) – the desired number of successes. It must be a non-negative integer.
  3. Enter the probability of success (p) – the probability of a single trial being a success. This value should be between 0 and 1.
  4. Click the “Calculate” button to obtain the result.

Interpreting the Results

The calculator will provide you with the calculated probability based on the chosen type of calculation. The results are expressed as a decimal number between 0 and 1, representing the likelihood of reaching the specified number of successes in the given number of trials.


The negative binomial distribution has applications in various fields:

  • Quality Control: Analyzing the number of defective items in a sample until a certain number of defects is reached.
  • Finance: Estimating the number of unsuccessful trades until a set number of profitable trades are achieved.
  • Customer Service: Predicting the number of customer interactions until achieving a specific number of successful resolutions.
  • Biostatistics: Studying the number of attempts to find a specific rare event, such as a disease diagnosis.

The Negative Binomial Distribution Calculator is a valuable tool for performing these probability calculations efficiently and accurately.

By entering the appropriate values and type of calculation, you can quickly assess the probabilities associated with reaching a certain number of successes in repeated trials.