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Negative Binomial Distribution Calculator

The negative binomial distribution calculator determines the simple and cumulative probabilities of a given distribution.

Probabilities:

How to Use the Negative Binomial Distribution Calculator?

  1. First, enter the probability of success on a trial (p) and the number of successes (r) and failures (k).
  2. Click the 'Calculate' button to generate probability results.
  3. The tool returns the simple and cumulative probabilities associated with the negative binomial distribution. The tool also finds the mean, variance, and standard deviation of the given inputs.

How to Calculate?

The probability P(X = k) for a negative binomial distribution is calculated using the following formula:

P(X = k) = (
k+r-1
r-1
 ) × (1 - p)k × pr
  • x = 0, 1, 2, ...
  • 0 < p ≤ 1

The mean, variance, and standard deviation are calculated using the following formulas:

Mean (μ) =  
r × (1 - p)
p
Variance (σ2) =  
r × (1 - p)
p2
SD (σ) =   √
r × (1 - p)
p2

Where,
p = Probability of success,
r = Number of successes,
k = Number of failures before the rth success,
SD = Standard deviation.

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