Everything about Negative multinomial distribution

🧭 Start here: a 6-step reading path

1. Read the overview: Negative multinomial distributionA 5-minute orientation
2. Skim a recent paper: Moments of the Negative Multinomial DistributionInfluential work since 2022
3. Pick up a classic book: Discrete mathematicsThe most-reprinted book on the subject
4. Read the landmark paper: Negative multinomial distributionCited 78 times
5. Go sideways: Dirichlet negative multinomial distributionA closely related topic
6. Go sideways: Logit-normal distributionA closely related topic

🏆 Landmark papers (most cited)

• Negative multinomial distribution

  Masaaki Sibuya, Isao Yoshimura, Ryoichi Shimizu · 1964 · Annals of the Institute of Statistical Mathematics · 78 citations

• On the compound negative multinomial distribution and correlations among inversely sampled pollen counts

  JAMES E. MOSIMANN · 1963 · Biometrika · 56 citations

• Integral expressions for tail probabilities of the multinomial and negative multinomial distributions

  I. Olkin, M. Sobel · 1965 · Biometrika · 45 citations

• Log-Linear Modeling with the Negative Multinomial Distribution

  Lance A. Waller, Daniel Zelterman · 1997 · Biometrics · 17 citations

• q-Multinomial and negativeq-multinomial distributions

  Charalambos A. Charalambides · 2020 · Communications in Statistics - Theory and Methods · 14 citations

• Orthogonal polynomials on the negative multinomial distribution

  R.C. Griffiths · 1975 · Journal of Multivariate Analysis · 12 citations

• A characterization of multinomial and negative multinomial distributions

  K. G. Janardan · 1974 · Scandinavian Actuarial Journal · 9 citations

• Integral expressions for tail probabilities of the negative multinomial distribution

  S. W. Joshi · 1975 · Annals of the Institute of Statistical Mathematics · 8 citations

🆕 Influential since 2022

• Moments of the Negative Multinomial Distribution

  Frédéric Ouimet · 2023 · Mathematical and Computational Applications · 1 citations

• New and fast closed-form efficient estimators for the negative multinomial distribution

  Jun Zhao, Yun-beom Lee, Hyoung-Moon Kim · 2025 · Communications in Statistics - Theory and Methods · 1 citations

• Domain of existence of the Laplace transform of negative multinomial distributions and simulations

  Philippe Bernardoff · 2023 · Statistics & Probability Letters · 1 citations

📚 Books worth reading

• Discrete mathematicsNorman Biggs · 1985
• Introduction to Probability and StatisticsJ. Susan Milton, Jesse C. Arnold · 1990
• Statistical models and control charts for high-quality processesM. Xie, Min Xie · 2002
• Elementary algebraHenry Sinclair Hall · 1895
• 📕Orthogonal polynomials on the negative multinomial distributionRobert C. Griffiths · 1972
• Probability and statistics for engineers and scientistsAnthony Hayter · 2012
• Introduction to probability and statisticsJ. Susan Milton, Jesse C. Arnold · 2002
• Essentials of StatisticsDavid Brink · 2013

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

• Dirichlet negative multinomial distribution In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is…
• Logit-normal distribution In probability theory, a logit-normal distribution is a probability distribution of a random variable whose logit has a normal distribution. If Y is a…
• Complex normal distribution In probability theory, the family of complex normal distributions, denoted C N {\displaystyle {\mathcal {CN}}} or N C {\displaystyle {\mathcal {N}}_{\mathcal…
• Karush–Kuhn–Tucker conditions In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes…
• Jackson network In queueing theory, a discipline within the mathematical theory of probability, a Jackson network (sometimes called a Jacksonian network) is a class of…
• Categorical distribution In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete…
• Natural exponential family In probability and statistics, a natural exponential family (NEF) is a class of probability distributions that is a special case of an exponential family…
• Multivariate t-distribution In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization…