Probability Negative Binomial Calculator
Probability negative binomial is a discrete probability distribution that expresses the probability of a certain number of successes in a sequence of independent Bernoulli trials before a specified number of failures occurs. Understanding and calculating this probability is crucial in various fields, including statistics, finance, and engineering.
How to Use This Calculator
- Enter the values for ‘r’ (number of successes), ‘p’ (probability of success), and ‘n’ (number of trials).
- Click ‘Calculate’.
- The result will appear below the calculator, and a chart will be generated to visualize the data.
Formula & Methodology
The probability mass function (PMF) of the negative binomial distribution is given by:
P(X = k; r, p) = (Γ(r + k) / (Γ(r) * k!)) * ((1 – p)^r * p^k)
Where:
- k is the number of successes.
- r is the number of trials until the first failure.
- p is the probability of success on each trial.
- Γ represents the gamma function.
Real-World Examples
Data & Statistics
Expert Tips
- Understand the difference between negative binomial and Poisson distributions.
- Be aware of the assumptions made when using the negative binomial distribution.
- Consider using a goodness-of-fit test to validate the use of the negative binomial distribution for your data.