---
references:
- id: Blaker2000Confidence
  accessed:
    - year: 2015
      month: 12
      day: 4
  author:
    - family: Blaker
      given: Helge
  citation-key: Blaker2000Confidence
  container-title: The Canadian Journal of Statistics / La Revue Canadienne de Statistique
  container-title-short: The Canadian Journal of Statistics / La Revue Canadienne de Statistique
  DOI: 10.2307/3315916
  ISSN: 0319-5724
  issue: '4'
  issued:
    - year: 2000
  page: 783-798
  title: >-
    Confidence Curves and Improved Exact Confidence Intervals for Discrete
    Distributions
  type: article-journal
  URL: >-
    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.9682&rep=rep1&type=pdf
  volume: '28'

- id: Burridge2013Cascade
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Burridge
      given: James
  citation-key: Burridge2013Cascade
  container-title: arXiv:1304.3741 [math]
  issued:
    - year: 2013
      month: 4
      day: 12
  title: Cascade sizes in a branching process with Gamma distributed generations
  type: article-journal
  URL: http://arxiv.org/abs/1304.3741

- id: Burridge2013Crossover
  accessed:
    - year: 2020
      month: 2
      day: 4
  author:
    - family: Burridge
      given: James
  citation-key: Burridge2013Crossover
  container-title: Physical Review E
  container-title-short: Phys. Rev. E
  DOI: 10.1103/PhysRevE.88.032124
  issue: '3'
  issued:
    - year: 2013
      month: 9
      day: 18
  page: '032124'
  PMID: '24125230'
  title: Crossover behavior in driven cascades
  type: article-journal
  URL: http://arxiv.org/abs/1308.4301
  volume: '88'

- id: Cao2015Poissona
  accessed:
    - year: 2015
      month: 6
      day: 25
  author:
    - family: Cao
      given: Yang
    - family: Xie
      given: Yao
  citation-key: Cao2015Poissona
  container-title: arXiv:1504.05229 [cs, math, stat]
  issued:
    - year: 2015
      month: 4
      day: 20
  title: Poisson Matrix Recovery and Completion
  type: article-journal
  URL: http://arxiv.org/abs/1504.05229

- id: Chatla2016Modeling
  accessed:
    - year: 2016
      month: 10
      day: 29
  author:
    - family: Chatla
      given: Suneel Babu
    - family: Shmueli
      given: Galit
  citation-key: Chatla2016Modeling
  container-title: arXiv:1610.08244 [stat]
  issued:
    - year: 2016
      month: 10
      day: 26
  title: 'Modeling Big Count Data: An IRLS Framework for CMP Regression and GAM'
  type: article-journal
  URL: http://arxiv.org/abs/1610.08244

- id: Consul1972Use
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Consul
      given: P.
    - family: Shenton
      given: L.
  citation-key: Consul1972Use
  container-title: SIAM Journal on Applied Mathematics
  container-title-short: SIAM J. Appl. Math.
  DOI: 10.1137/0123026
  ISSN: 0036-1399
  issue: '2'
  issued:
    - year: 1972
      month: 9
      day: 1
  page: 239-248
  title: >-
    Use of Lagrange Expansion for Generating Discrete Generalized Probability
    Distributions
  type: article-journal
  volume: '23'

- id: Consul1973Generalization
  accessed:
    - year: 2016
      month: 4
      day: 7
  author:
    - family: Consul
      given: P. C.
    - family: Jain
      given: G. C.
  citation-key: Consul1973Generalization
  container-title: Technometrics
  container-title-short: Technometrics
  DOI: 10.1080/00401706.1973.10489112
  ISSN: 0040-1706
  issue: '4'
  issued:
    - year: 1973
      month: 11
      day: 1
  page: 791-799
  title: A Generalization of the Poisson Distribution
  type: article-journal
  volume: '15'

- id: Consul1973Interesting
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Consul
      given: P. C.
    - family: Shenton
      given: L. R.
  citation-key: Consul1973Interesting
  container-title: Communications in Statistics
  DOI: 10.1080/03610927308827073
  ISSN: 0090-3272
  issue: '3'
  issued:
    - year: 1973
      month: 1
      day: 1
  page: 263-272
  title: Some interesting properties of Lagrangian distributions
  type: article-journal
  volume: '2'

- id: Consul1975Probabilistic
  accessed:
    - year: 2016
      month: 6
      day: 1
  author:
    - family: Consul
      given: P. C.
    - family: Shenton
      given: L. R.
  citation-key: Consul1975Probabilistic
  collection-number: '17'
  collection-title: NATO Advanced Study Institutes Series
  container-title: A Modern Course on Statistical Distributions in Scientific Work
  DOI: 10.1007/978-94-010-1842-5_5
  editor:
    - family: Patil
      given: G. P.
    - family: Kotz
      given: S.
    - family: Ord
      given: J. K.
  ISBN: 978-94-010-1844-9 978-94-010-1842-5
  issued:
    - year: 1975
  language: en
  page: 41-57
  publisher: Springer Netherlands
  title: >-
    On the Probabilistic Structure and Properties of Discrete Lagrangian
    Distributions
  type: chapter
  URL: http://link.springer.com/chapter/10.1007/978-94-010-1842-5_5

- id: Consul1984Maximum
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Consul
      given: P.C.
    - family: Shoukri
      given: M. M.
  citation-key: Consul1984Maximum
  container-title: Communications in Statistics - Theory and Methods
  DOI: 10.1080/03610928408828776
  ISSN: 0361-0926
  issue: '12'
  issued:
    - year: 1984
      month: 1
      day: 1
  page: 1533-1547
  title: Maximum likelihood estimation for the generalized poisson distribution
  type: article-journal
  volume: '13'

- id: Consul1988Chance
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Consul
      given: P.C.
    - family: Shoukri
      given: M.M.
  citation-key: Consul1988Chance
  container-title: American Journal of Mathematical and Management Sciences
  DOI: 10.1080/01966324.1988.10737237
  ISSN: 0196-6324, 2325-8454
  issue: 1-2
  issued:
    - year: 1988
      month: 1
  language: en
  page: 181-202
  title: Some Chance Mechanisms Related to a Generalized Poisson Probability Model
  type: article-journal
  volume: '8'

- id: Consul1988Generalized
  author:
    - family: Consul
      given: P. C.
  citation-key: Consul1988Generalized
  event-place: New York
  ISBN: 978-0-8247-7863-7
  issued:
    - year: 1988
      month: 12
      day: 22
  language: English
  number-of-pages: '320'
  publisher: CRC Press
  publisher-place: New York
  title: Generalized Poisson Distributions
  type: book

- id: Consul1989Minimum
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Consul
      given: P. C.
    - family: Felix
      given: Famoye
  citation-key: Consul1989Minimum
  container-title: Statistics
  DOI: 10.1080/02331888908802188
  ISSN: 0233-1888
  issue: '3'
  issued:
    - year: 1989
      month: 1
      day: 1
  page: 407-415
  title: >-
    Minimum variance unbiased estimation for the lagrange power series
    distributions
  type: article-journal
  volume: '20'

- id: Consul1992Generalized
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Consul
      given: P. C.
    - family: Famoye
      given: Felix
  citation-key: Consul1992Generalized
  container-title: Communications in Statistics - Theory and Methods
  DOI: 10.1080/03610929208830766
  ISSN: 0361-0926
  issue: '1'
  issued:
    - year: 1992
      month: 1
      day: 1
  page: 89-109
  title: Generalized poisson regression model
  type: article-journal
  volume: '21'

- id: Consul2006Lagrangian
  author:
    - family: Consul
      given: P. C.
    - family: Famoye
      given: Felix
  call-number: QA273.6 .C664 2006
  citation-key: Consul2006Lagrangian
  event-place: Boston
  ISBN: 978-0-8176-4365-2 978-0-8176-4477-2
  issued:
    - year: 2006
  number-of-pages: '352'
  publisher: Birkhäuser
  publisher-place: Boston
  title: Lagrangian probability distributions
  type: book
  URL: >-
    https://books.google.com/books/about/Lagrangian_Probability_Distributions.html?id=UGbkIwT63qsC

- id: Cox1983Remarks
  accessed:
    - year: 2015
      month: 6
      day: 24
  author:
    - family: Cox
      given: D. R.
  citation-key: Cox1983Remarks
  container-title: Biometrika
  container-title-short: Biometrika
  DOI: 10.1093/biomet/70.1.269
  ISSN: 0006-3444, 1464-3510
  issue: '1'
  issued:
    - year: 1983
      month: 1
      day: 4
  language: en
  page: 269-274
  title: Some remarks on overdispersion
  type: article-journal
  volume: '70'

- id: Cui2009New
  accessed:
    - year: 2015
      month: 6
      day: 2
  author:
    - family: Cui
      given: Yunwei
    - family: Lund
      given: Robert
  citation-key: Cui2009New
  container-title: Biometrika
  container-title-short: Biometrika
  DOI: 10.1093/biomet/asp057
  ISSN: 0006-3444, 1464-3510
  issue: '4'
  issued:
    - year: 2009
      month: 1
      day: 12
  language: en
  page: 781-792
  publisher: Oxford Academic
  title: A new look at time series of counts
  type: article-journal
  volume: '96'

- id: Doray2009Simple
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Doray
      given: Louis G.
    - family: Jiang
      given: Shu Mei
    - family: Luong
      given: Andrew
  citation-key: Doray2009Simple
  container-title: Communications in Statistics - Simulation and Computation
  DOI: 10.1080/03610910903202089
  ISSN: 0361-0918
  issue: '9'
  issued:
    - year: 2009
      month: 10
      day: 1
  page: 2004-2017
  title: >-
    Some Simple Method of Estimation for the Parameters of the Discrete Stable
    Distribution with the Probability Generating Function
  type: article-journal
  URL: http://www.dms.umontreal.ca/~doray/jiang.pdf
  volume: '38'

- id: Dwass1969Total
  accessed:
    - year: 2015
      month: 12
      day: 28
  author:
    - family: Dwass
      given: Meyer
  citation-key: Dwass1969Total
  container-title: Journal of Applied Probability
  container-title-short: Journal of Applied Probability
  DOI: 10.2307/3212112
  ISSN: 0021-9002
  issue: '3'
  issued:
    - year: 1969
  page: 682-686
  publisher: Cambridge University Press
  title: The Total Progeny in a Branching Process and a Related Random Walk
  type: article-journal
  volume: '6'

- id: Felix1992Estimation
  accessed:
    - year: 2019
      month: 10
      day: 13
  author:
    - family: Felix
      given: Famoye
    - family: Lee
      given: Carl M.-S.
  citation-key: Felix1992Estimation
  container-title: Communications in Statistics - Simulation and Computation
  DOI: 10.1080/03610919208813013
  ISSN: 0361-0918
  issue: '1'
  issued:
    - year: 1992
      month: 1
      day: 1
  page: 173-188
  title: Estimation of generalized poisson distribution
  type: article-journal
  volume: '21'

- id: Goldstein2004Problems
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Goldstein
      given: M. L.
    - family: Morris
      given: S. A.
    - family: Yen
      given: G. G.
  citation-key: Goldstein2004Problems
  container-title: The European Physical Journal B - Condensed Matter and Complex Systems
  container-title-short: Eur. Phys. J. B
  DOI: 10.1140/epjb/e2004-00316-5
  ISSN: 1434-6028, 1434-6036
  issue: '2'
  issued:
    - year: 2004
      month: 9
  language: en
  page: 255-258
  title: Problems with fitting to the power-law distribution
  type: article-journal
  URL: http://arxiv.org/abs/cond-mat/0402322
  volume: '41'

- id: Greenwood1920Inquiry
  accessed:
    - year: 2015
      month: 11
      day: 28
  author:
    - family: Greenwood
      given: Major
    - family: Yule
      given: G. Udny
  citation-key: Greenwood1920Inquiry
  container-title: Journal of the Royal Statistical Society
  container-title-short: Journal of the Royal Statistical Society
  DOI: 10.2307/2341080
  ISSN: 0952-8385
  issue: '2'
  issued:
    - year: 1920
  page: 255-279
  title: >-
    An Inquiry into the Nature of Frequency Distributions Representative of
    Multiple Happenings with Particular Reference to the Occurrence of Multiple
    Attacks of Disease or of Repeated Accidents
  type: article-journal
  volume: '83'

- id: Haight1960BorelTanner
  accessed:
    - year: 2021
      month: 8
      day: 3
  author:
    - family: Haight
      given: Frank A.
    - family: Breuer
      given: Melvin Allen
  citation-key: Haight1960BorelTanner
  container-title: Biometrika
  container-title-short: Biometrika
  DOI: 10.1093/biomet/47.1-2.143
  ISSN: 0006-3444
  issue: 1-2
  issued:
    - year: 1960
      month: 6
      day: 1
  page: 143-150
  title: The Borel-Tanner distribution
  type: article-journal
  volume: '47'

- id: Imoto2016Properties
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Imoto
      given: Tomoaki
  citation-key: Imoto2016Properties
  container-title: Communications in Statistics - Theory and Methods
  DOI: 10.1080/03610926.2013.835414
  ISSN: 0361-0926
  issue: '3'
  issued:
    - year: 2016
      month: 2
      day: 1
  page: 712-721
  title: Properties of Lagrangian distributions
  type: article-journal
  volume: '45'

- id: Janardan1984Moments
  accessed:
    - year: 2016
      month: 6
      day: 1
  author:
    - family: Janardan
      given: K.
  citation-key: Janardan1984Moments
  container-title: SIAM Journal on Applied Mathematics
  container-title-short: SIAM J. Appl. Math.
  DOI: 10.1137/0144061
  ISSN: 0036-1399
  issue: '4'
  issued:
    - year: 1984
      month: 8
      day: 1
  page: 854-868
  title: Moments of Certain Series Distributions and Their Applications
  type: article-journal
  volume: '44'

- id: Johnson2005Univariate
  author:
    - family: Johnson
      given: Norman Lloyd
    - family: Kemp
      given: Adrienne W.
    - family: Kotz
      given: Samuel
  call-number: QA273.6 .J64 2005
  citation-key: Johnson2005Univariate
  edition: 3rd ed
  event-place: Hoboken, N.J
  ISBN: 978-0-471-27246-5
  issued:
    - year: 2005
  number-of-pages: '646'
  publisher: Wiley
  publisher-place: Hoboken, N.J
  title: Univariate discrete distributions
  type: book

- id: Karlis2023Models
  accessed:
    - year: 2023
      month: 3
      day: 12
  author:
    - family: Karlis
      given: Dimitris
    - family: Mamode Khan
      given: Naushad
  citation-key: Karlis2023Models
  container-title: Annual Review of Statistics and Its Application
  DOI: 10.1146/annurev-statistics-032921-022516
  issue: '1'
  issued:
    - year: 2023
  page: 297-323
  title: Models for Integer Data
  type: article-journal
  volume: '10'

- id: Lee2008Continuous
  accessed:
    - year: 2015
      month: 12
      day: 4
  author:
    - family: Lee
      given: W. H.
    - family: Hopcraft
      given: K. I.
    - family: Jakeman
      given: E.
  citation-key: Lee2008Continuous
  container-title: Physical Review E
  container-title-short: Phys. Rev. E
  DOI: 10.1103/PhysRevE.77.011109
  issue: '1'
  issued:
    - year: 2008
      month: 1
      day: 9
  page: '011109'
  title: Continuous and discrete stable processes
  type: article-journal
  URL: https://www.academia.edu/171266/Continuous_and_discrete_stable_processes
  volume: '77'

- id: Lee2010Continuous
  accessed:
    - year: 2019
      month: 9
      day: 22
  author:
    - family: Lee
      given: Wai Ha
  citation-key: Lee2010Continuous
  genre: PhD
  issued:
    - year: 2010
      month: 7
      day: 19
  language: en
  title: Continuous and discrete properties of stochastic processes
  type: thesis
  URL: http://eprints.nottingham.ac.uk/11194/

- id: Li2010Generalized
  author:
    - family: Li
      given: S
    - family: Famoye
      given: F
    - family: Lee
      given: C
  citation-key: Li2010Generalized
  container-title: Journal of Probability and Statistical Science
  issue: '1'
  issued:
    - year: 2010
  page: 113-123
  title: On the generalized Lagrangian probability distributions
  type: article-journal
  volume: '8'

- id: LloydSmith2007Maximum
  accessed:
    - year: 2015
      month: 11
      day: 28
  author:
    - family: Lloyd-Smith
      given: James O.
  citation-key: LloydSmith2007Maximum
  container-title: PLoS ONE
  container-title-short: PLoS ONE
  DOI: 10.1371/journal.pone.0000180
  issue: '2'
  issued:
    - year: 2007
      month: 2
      day: 14
  page: e180
  title: >-
    Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter
    for Highly Overdispersed Data, with Applications to Infectious Diseases
  type: article-journal
  URL: http://dx.plos.org/10.1371/journal.pone.0000180
  volume: '2'

- id: Mutafchiev1995Local
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Mutafchiev
      given: Ljuben
  citation-key: Mutafchiev1995Local
  container-title: aequationes mathematicae
  container-title-short: Aeq. Math.
  DOI: 10.1007/BF01827929
  ISSN: 0001-9054, 1420-8903
  issue: '1'
  issued:
    - year: 1995
      month: 2
  language: en
  page: 57-85
  title: Local limit approximations for Lagrangian distributions
  type: article-journal
  volume: '49'

- id: Neyman1965Certain
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Neyman
      given: Jerzy
  citation-key: Neyman1965Certain
  container-title: 'Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)'
  container-title-short: 'Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)'
  ISSN: 0581-572X
  issue: 2/4
  issued:
    - year: 1965
  page: 249-258
  title: Certain Chance Mechanisms Involving Discrete Distributions
  type: article-journal
  URL: http://www.jstor.org/stable/25049369
  volume: '27'

- id: Nolan1997Numerical
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Nolan
      given: John P.
  citation-key: Nolan1997Numerical
  container-title: Communications in Statistics. Stochastic Models
  DOI: 10.1080/15326349708807450
  ISSN: 0882-0287
  issue: '4'
  issued:
    - year: 1997
      month: 1
  language: en
  page: 759-774
  title: Numerical calculation of stable densities and distribution functions
  type: article-journal
  volume: '13'

- id: Nolan1997Parameter
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Nolan
      given: J.P.
  citation-key: Nolan1997Parameter
  DOI: 10.1109/ACSSC.1997.680366
  ISBN: 0-8186-8316-3
  issued:
    - year: 1997
  page: 443-447
  publisher: IEEE Comput. Soc
  title: Parameter estimation and data analysis for stable distributions
  type: paper-conference
  volume: '1'

- id: Nolan2001Maximum
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Nolan
      given: John P.
  citation-key: Nolan2001Maximum
  container-title: Lévy Processes
  DOI: 10.1007/978-1-4612-0197-7_17
  editor:
    - family: Barndorff-Nielsen
      given: Ole E.
    - family: Resnick
      given: Sidney I.
    - family: Mikosch
      given: Thomas
  ISBN: 978-1-4612-6657-0 978-1-4612-0197-7
  issued:
    - year: 2001
  language: en
  page: 379-400
  publisher: Birkhäuser Boston
  title: Maximum Likelihood Estimation and Diagnostics for Stable Distributions
  type: chapter
  URL: >-
    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.184.6751&rep=rep1&type=pdf

- id: Pitman1998Enumerations
  accessed:
    - year: 2021
      month: 8
      day: 3
  author:
    - family: Pitman
      given: Jim
  citation-key: Pitman1998Enumerations
  collection-title: >-
    DIMACS Series in Discrete Mathematics and                        
    Theoretical Computer Science
  container-title: Microsurveys in Discrete Probability
  DOI: 10.1090/dimacs/041
  editor:
    - family: Aldous
      given: David
    - family: Propp
      given: James
  event-place: Providence, Rhode                     Island
  ISBN: 978-0-8218-0827-6 978-1-4704-3999-6
  issued:
    - year: 1998
      month: 5
      day: 5
  language: en
  publisher: American Mathematical                     Society
  publisher-place: Providence, Rhode                     Island
  title: >-
    Enumerations of trees and forests related to branching processes and random
    walks
  type: chapter
  URL: http://d-nb.info/977967352/04
  volume: '41'

- id: Saha2005Biascorrected
  author:
    - family: Saha
      given: Krishna
    - family: Paul
      given: Sudhir
  citation-key: Saha2005Biascorrected
  container-title: Biometrics
  container-title-short: Biometrics
  DOI: 10.1111/j.0006-341X.2005.030833.x
  ISSN: 0006-341X
  issue: '1'
  issued:
    - year: 2005
      month: 3
  language: eng
  page: 179-185
  PMID: '15737091'
  title: >-
    Bias-corrected maximum likelihood estimator of the negative binomial
    dispersion parameter
  type: article-journal
  URL: https://ideas.repec.org/a/bla/biomet/v61y2005i1p179-185.html
  volume: '61'

- id: Schein2016PoissonGamma
  author:
    - family: Schein
      given: Aaron
    - family: Wallach
      given: Hanna
    - family: Zhou
      given: Mingyuan
  citation-key: Schein2016PoissonGamma
  container-title: Advances In Neural Information Processing Systems
  issued:
    - year: 2016
  page: 5006–5014
  title: Poisson-Gamma dynamical systems
  type: paper-conference
  URL: http://papers.nips.cc/paper/6082-poisson-gamma-dynamical-systems

- id: Shmueli2005Useful
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Shmueli
      given: Galit
    - family: Minka
      given: Thomas P.
    - family: Kadane
      given: Joseph B.
    - family: Borle
      given: Sharad
    - family: Boatwright
      given: Peter
  citation-key: Shmueli2005Useful
  container-title: Journal of the Royal Statistical Society. Series C (Applied Statistics)
  container-title-short: Journal of the Royal Statistical Society. Series C (Applied Statistics)
  ISSN: 0035-9254
  issue: '1'
  issued:
    - year: 2005
  page: 127-142
  title: >-
    A Useful Distribution for Fitting Discrete Data: Revival of the
    Conway-Maxwell-Poisson Distribution
  type: article-journal
  URL: >-
    http://www.ics.uci.edu/~johnsong/papers/Shmueli%20et.%20al%20-%20A%20Useful%20Distribution%20for%20Fitting%20Discrete%20Data%20(revival%20of%20the%20Conway-Maxwell-Poisson%20distribution).pdf
  volume: '54'

- id: Shoukri1987Chance
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Shoukri
      given: M. M.
    - family: Consul
      given: P. C.
  citation-key: Shoukri1987Chance
  container-title: Biostatistics
  editor:
    - family: MacNeill
      given: Ian B.
    - family: Umphrey
      given: Gary J.
    - family: Donner
      given: Allan
    - family: Jandhyala
      given: V. Krishna
  event-place: Dordrecht
  ISBN: 978-94-010-8626-4 978-94-009-4794-8
  issued:
    - year: 1987
  page: 259-268
  publisher: Springer Netherlands
  publisher-place: Dordrecht
  title: Some Chance Mechanisms Generating the Generalized Poisson Probability Models
  type: chapter
  URL: http://link.springer.com/10.1007/978-94-009-4794-8_15

- id: Sibuya1994Aspects
  accessed:
    - year: 2016
      month: 3
      day: 9
  author:
    - family: Sibuya
      given: Masaaki
    - family: Miyawaki
      given: Norihiko
    - family: Sumita
      given: Ushio
  citation-key: Sibuya1994Aspects
  container-title: Journal of Applied Probability
  container-title-short: Journal of Applied Probability
  DOI: 10.2307/3214956
  ISSN: 0021-9002
  issued:
    - year: 1994
  page: 185-197
  title: Aspects of Lagrangian Probability Distributions
  type: article-journal
  volume: '31'

- id: Soltani2009Class
  accessed:
    - year: 2015
      month: 12
      day: 6
  author:
    - family: Soltani
      given: A. R.
    - family: Shirvani
      given: A.
    - family: Alqallaf
      given: F.
  citation-key: Soltani2009Class
  container-title: Statistics & Probability Letters
  container-title-short: Statistics & Probability Letters
  DOI: 10.1016/j.spl.2009.03.030
  ISSN: 0167-7152
  issue: '14'
  issued:
    - year: 2009
      month: 7
      day: 15
  page: 1608-1614
  title: A class of discrete distributions induced by stable laws
  type: article-journal
  volume: '79'

- id: Steutel1979Discrete
  accessed:
    - year: 2015
      month: 6
      day: 17
  author:
    - family: Steutel
      given: F. W.
    - family: Harn
      given: K.
      non-dropping-particle: van
  citation-key: Steutel1979Discrete
  container-title: The Annals of Probability
  container-title-short: Ann. Probab.
  DOI: 10.1214/aop/1176994950
  ISSN: 0091-1798, 2168-894X
  issue: '5'
  issued:
    - year: 1979
      month: 10
  language: EN
  page: 893-899
  title: Discrete Analogues of Self-Decomposability and Stability
  type: article-journal
  volume: '7'

- id: Steyvers2005LargeScale
  accessed:
    - year: 2012
      month: 10
      day: 2
  author:
    - family: Steyvers
      given: Mark
    - family: Tenenbaum
      given: Joshua B.
  citation-key: Steyvers2005LargeScale
  container-title: Cognitive Science
  DOI: 10.1207/s15516709cog2901_3
  ISSN: 1551-6709
  issue: '1'
  issued:
    - year: 2005
  language: en
  page: 41-78
  title: >-
    The Large-Scale Structure of Semantic Networks: Statistical Analyses and a
    Model of Semantic Growth
  type: article-journal
  URL: http://arxiv.org/abs/cond-mat/0110012
  volume: '29'

- id: Tanner1961Derivation
  accessed:
    - year: 2021
      month: 8
      day: 3
  author:
    - family: Tanner
      given: J. C.
  citation-key: Tanner1961Derivation
  container-title: Biometrika
  container-title-short: Biometrika
  DOI: 10.1093/biomet/48.1-2.222
  ISSN: 0006-3444
  issue: 1-2
  issued:
    - year: 1961
      month: 6
      day: 1
  page: 222-224
  title: A derivation of the Borel distribution
  type: article-journal
  volume: '48'

- id: Tsou2006Robust
  accessed:
    - year: 2015
      month: 6
      day: 24
  author:
    - family: Tsou
      given: Tsung-Shan
  citation-key: Tsou2006Robust
  container-title: Journal of Statistical Planning and Inference
  container-title-short: Journal of Statistical Planning and Inference
  DOI: 10.1016/j.jspi.2004.12.008
  ISSN: 0378-3758
  issue: '9'
  issued:
    - year: 2006
      month: 9
      day: 1
  page: 3173-3186
  title: Robust Poisson regression
  type: article-journal
  volume: '136'

- id: Tuenter2000Generalized
  accessed:
    - year: 2016
      month: 4
      day: 7
  author:
    - family: Tuenter
      given: Hans J. H.
  citation-key: Tuenter2000Generalized
  container-title: Statistica Neerlandica
  DOI: 10.1111/1467-9574.00147
  ISSN: 0039-0402, 1467-9574
  issue: '3'
  issued:
    - year: 2000
      month: 11
  page: 374-376
  title: On the Generalized Poisson Distribution
  type: article-journal
  URL: http://arxiv.org/abs/math/0606238
  volume: '54'

- id: Turkman2014Models
  accessed:
    - year: 2015
      month: 6
      day: 16
  author:
    - family: Turkman
      given: Kamil Feridun
    - family: Scotto
      given: Manuel González
    - family: Bermudez
      given: Patrícia de Zea
  citation-key: Turkman2014Models
  container-title: Non-Linear Time Series
  ISBN: 978-3-319-07027-8 978-3-319-07028-5
  issued:
    - year: 2014
  language: en
  page: 199-244
  publisher: Springer International Publishing
  title: Models for Integer-Valued Time Series
  type: chapter

- id: vanHarn1982Selfdecomposable
  accessed:
    - year: 2015
      month: 6
      day: 17
  author:
    - family: Harn
      given: K.
      non-dropping-particle: van
    - family: Steutel
      given: F. W.
    - family: Vervaat
      given: W.
  citation-key: vanHarn1982Selfdecomposable
  container-title: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
  container-title-short: Z. Wahrscheinlichkeitstheorie verw Gebiete
  DOI: 10.1007/BF00537228
  ISSN: 0044-3719, 1432-2064
  issue: '1'
  issued:
    - year: 1982
      month: 3
      day: 1
  language: en
  page: 97-118
  title: Self-decomposable discrete distributions and branching processes
  type: article-journal
  volume: '61'

- id: vanHarn1993Stability
  accessed:
    - year: 2015
      month: 6
      day: 17
  author:
    - family: Harn
      given: K.
      non-dropping-particle: van
    - family: Steutel
      given: F. W.
  citation-key: vanHarn1993Stability
  container-title: Stochastic Processes and their Applications
  DOI: 10.1016/0304-4149(93)90070-K
  ISSN: 0304-4149, 0304-4149
  issue: '2'
  issued:
    - year: 1993
  page: 209–230
  title: >-
    Stability equations for processes with stationary independent increments
    using branching processes and Poisson mixtures
  type: article-journal
  URL: https://ideas.repec.org/a/eee/spapps/v45y1993i2p209-230.html
  volume: '45'

- id: Wedel2003Factor
  accessed:
    - year: 2015
      month: 4
      day: 17
  author:
    - family: Wedel
      given: Michel
    - family: Böckenholt
      given: Ulf
    - family: Kamakura
      given: Wagner A.
  citation-key: Wedel2003Factor
  container-title: Journal of Multivariate Analysis
  container-title-short: Journal of Multivariate Analysis
  DOI: 10.1016/S0047-259X(03)00020-4
  ISSN: 0047-259X
  issue: '2'
  issued:
    - year: 2003
      month: 11
  page: 356-369
  title: Factor models for multivariate count data
  type: article-journal
  volume: '87'

- id: Wolpert2021Markov
  accessed:
    - year: 2021
      month: 12
      day: 21
  author:
    - family: Wolpert
      given: Robert L.
    - family: Brown
      given: Lawrence D.
  citation-key: Wolpert2021Markov
  container-title: arXiv:2105.14591 [math]
  issued:
    - year: 2021
      month: 5
      day: 30
  title: >-
    Markov Infinitely-Divisible Stationary Time-Reversible Integer-Valued
    Processes
  type: article-journal
  URL: http://arxiv.org/abs/2105.14591
...
