Advanced search
Publication Cover
The American Statistician Volume 71, 2017 - Issue 1
Submit an article Journal homepage
857
Views
13
CrossRef citations to date
0
Altmetric
GENERAL

Bridging the Gap: A Generalized Stochastic Process for Count Data

Li ZhuCAC Fund, Shanghai, China;Department of Mathematics and Statistics, Georgetown University, Washington, DC
,
Kimberly F. SellersDepartment of Mathematics and Statistics, Georgetown University, Washington, DC;Center for Statistical Research & Methodology, U.S. Census Bureau, Washington, DCCorrespondence[email protected]
,
Darcy Steeg MorrisCenter for Statistical Research & Methodology, U.S. Census Bureau, Washington, DC
&
Galit ShmueliInstitute of Service Science, National Tsing Hua University, Taiwan
Pages 71-80 | Received 01 Aug 2014, Published online: 20 Mar 2017

References

  • Balakrishnan, N., and Kozubowski, T. J. (2008), “A Class of Weighted Poisson Processes,” Statistics and Probability Letters, 78, 2346–2352.
  • Barndorff-Nielsen, O., and Yeo, G. F. (1969), “Negative Binomial Processes,” Journal of Applied Probability, 6, 633–647.
  • Brillinger, D. R. (1995), “Trend Analysis: Binary-Valued and Point Cases,” Stochastic Hydrology and Hydraulics, 9, 207–213.
  • Burnham, K. P., and Anderson, D. R. (2002), Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.), New York: Springer.
  • Canty, A., and Ripley, B. (2015), boot: Bootstrap Functions, Version 1.3-15. Available at http://cran.r-project.org/web/packages/boot/index.html
  • Chatfield, C., and Goodhardt, G. J. (1973), “A Consumer Purchasing Model with Erlang Inter-Purchase Time,” Journal of the American Statistical Association, 68, 828–835.
  • Çinlar, E. (1975), Introduction to Stochastic Processes, New York: Prentice-Hall, Inc.
  • Conway, R. W., and Maxwell, W. L. (1962), “A Queuing Model with State Dependent Service Rates,” Journal of Industrial Engineering, 12, 132–136.
  • Diggle, P. J., and Milne, R. K. (1983), “Binomial Quadrat Counts and Point Processes,” Scandinavian Journal of Statistics, 10, 257–267.
  • Durrett, R. (2004), Essentials of Stochastic Processes, New York: Springer.
  • Guttorp, P. (1995), Stochastic Modeling of Scientific Data, Boca Raton, FL: Chapman & Hall/CRC.
  • Johnson, N. L., Kemp, A. W., and Kotz, S. (2005), Univariate Discrete Distributions (3rd ed.), New York: Wiley.
  • Kannan, D. (1979), An Introduction to Stochastic Processes, New York: Elsevier North Holland.
  • Kokonendji, C. C., Mizère, D., and Balakrishnan, N. (2008), “Connections of the Poisson Weight Function to Overdispersion and Underdispersion,” Journal of Statistical Planning and Inference, 138, 1287–1296.
  • Sellers, K. F. (2012), “A Generalized Statistical Control Chart for Over- or Under-Dispersed Data,” Quality and Reliability Engineering International, 28, 59–65.
  • Sellers, K. F., Shmueli, G., and Borle, S. (2011), “The COM-Poisson Model for Count Data: A Survey of Methods and Applications,” Applied Stochastic Models in Business and Industry, 28, 104–116.
  • Sellers, K. F., and Shmueli, G. (2010), “A Flexible Regression Model for Count Data,” Annals of Applied Statistics, 4, 943–961.
  • ———— (2013), “Data Dispersion: Now You See it… Now You Don’t,” Communications in Statistics—Theory and Methods, 42, 3134–3147.
  • Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., and Boatwright, P. (2005), “A Useful Distribution for Fitting Discrete Data: Revival of the Conway-Maxwell-Poisson Distribution,” Applied Statistics—Journal of the Royal Statistical Society, Series C, 54, 127–142.
  • Soldatov, A. P. (2011), Underdetermined system, Encyclopedia of Mathematics Available at http://www.encyclopediaofmath.org/index.php?title=Underdetermined_system&oldid=16734.
  • Stephens, K. S. (2012), Reliability Data Analysis with Excel and Minitab, Milwaukee, WI: ASQ Quality Press.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.