On Ling's binomial and negative binomial distributions of order k

DOI10.1016/0167-7152(91)90115-8zbMath0728.60017OpenAlexW2004972051MaRDI QIDQ805052

Katuomi Hirano, Nobuhisa Kashiwagi, Hisataka Kuboki, Sigeo Aki

Publication date: 1991

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(91)90115-8

zbMATH Keywords

probability generating functionbinomial distributions of order k

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05)

Related Items (16)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Estimation of parameters in the discrete distributions of order k
• A generalized geometric distribution and some of its properties
• Discrete distributions of order k on a binary sequence
• Properties of the extended distributions of order k
• On binomial distributions of order k
• A new class of negative binomial distributions of order k
• On discrete distributions of order k
• Successes, runs and longest runs

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