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Everything about Negative binomial distribution

Probability distribution

In probability theory and statistics, the negative binomial distribution, also called a Pascal distribution, is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified/constant/fixed number of successes occur. For example, we can define rolling a 6 on some dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success. In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. Wikipedia →

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  1. Read the overview: Negative binomial distributionA 5-minute orientation
  2. Skim a recent paper: Evaluating alternative variations of Negative Binomial–Lindley distribution for modelling crash dataInfluential work since 2022
  3. Pick up a classic book: Negative Binomial RegressionThe most-reprinted book on the subject
  4. Read the landmark paper: THE NEGATIVE BINOMIAL DISTRIBUTIONCited 206 times
  5. Go sideways: Mixed Poisson distributionA closely related topic
  6. Go sideways: Poisson distributionA closely related topic

📖 Definitions

Noun A discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

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🆕 Influential since 2022

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