References

Agresti, A. 2013. Categorical Data Analysis. New York: Wiley.

Agresti, Alan. 2010. Analysis of Ordinal Categorical Data. 2nd ed. Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons. https://doi.org/10.1002/9780470594001.

Allaire, J. J., Charles Teague, Carlos Scheidegger, Yihui Xie, Christophe Dervieux, and Gordon Woodhull. 2025. “Quarto.” https://doi.org/10.5281/zenodo.5960048.

Argawu, Alemayehu Siffir, and Gizachew Gobebo Mekebo. 2023. “Zero-Inflated Poisson Regression Analysis of Factors Associated with Under-Five Mortality in Ethiopia Using 2019 Ethiopian Mini Demographic and Health Survey Data.” PLOS ONE 18 (11): e0291426. https://doi.org/10.1371/journal.pone.0291426.

Bellhouse, D. R. 2004. “The Reverend Thomas Bayes, FRS: A Biography to Celebrate the Tercentenary of His Birth.” Statistical Science 19 (1): 3–43. https://doi.org/10.1214/088342304000000189.

Bolker, Benjamin M., Mollie E. Brooks, Connie J. Clark, Shane W. Geange, John R. Poulsen, M. Henry H. Stevens, and Jada-Simone S. White. 2009. “Generalized Linear Mixed Models: A Practical Guide for Ecology and Evolution.” Trends in Ecology & Evolution 24 (3): 127–35. https://doi.org/10.1016/j.tree.2008.10.008.

Botton, Mark L. 2009. “The Ecological Importance of Horseshoe Crabs in Estuarine and Coastal Communities: A Review and Speculative Summary.” In Biology and Conservation of Horseshoe Crabs, edited by John T. Tanacredi, Mark L. Botton, and David R. Smith, 45–63. Boston, MA: Springer. https://doi.org/10.1007/978-0-387-89959-6_3.

Brent, Richard P. 1973. “Chapter 4: An Algorithm with Guaranteed Convergence for Finding a Zero of a Function.” In Algorithms for Minimization Without Derivatives. Englewood Cliffs, NJ: Prentice-Hall.

Brockmann, H. Jane. 1996. “Satellite Male Groups in Horseshoe Crabs, Limulus Polyphemus.” Ethology 102 (1): 1–21. https://doi.org/10.1111/j.1439-0310.1996.tb01099.x.

———. 2002. “An Experimental Approach to Altering Mating Tactics in Male Horseshoe Crabs (Limulus Polyphemus).” Behavioral Ecology 13 (2): 232–38. https://doi.org/10.1093/beheco/13.2.232.

Brockmann, H. Jane, and Matthew D. Smith. 2009. “Reproductive Competition and Sexual Selection in Horseshoe Crabs.” In Biology and Conservation of Horseshoe Crabs, edited by John T. Tanacredi, Mark L. Botton, and David R. Smith, 199–221. Boston, MA: Springer. https://doi.org/10.1007/978-0-387-89959-6_12.

Cameron, A. Colin, and Pravin K. Trivedi. 2013. Regression Analysis of Count Data. 2nd ed. Econometric Society Monographs. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9781139013567.

Casella, G., and R. Berger. 2024. Statistical Inference. Chapman & Hall/CRC Texts in Statistical Science. CRC Press. https://www.taylorfrancis.com/books/mono/10.1201/9781003456285/statistical-inference-roger-berger-george-casella.

Cauchy, Augustin-Louis. 1847. “Méthode Générale Pour La Résolution Des Systèmes d’équations Simultanées.” Comptes Rendus Hebdomadaires Des Séances de l’Académie Des Sciences 25: 536. https://gallica.bnf.fr/ark:/12148/bpt6k32298/f548.item.

Clark, Michael. 2022. “Generalized Additive Models.” https://m-clark.github.io/generalized-additive-models/.

Consul, P. C., and G. C. Jain. 1973. “A Generalization of the Poisson Distribution.” Technometrics 15 (4): 791–99. http://www.jstor.org/stable/1267389.

D’Agostino, Ralph B., and Michael A. Stephens, eds. 1986. Goodness-of-Fit Techniques. Vol. 68. Statistics: Textbooks and Monographs. New York: Marcel Dekker.

Dodge, Yadolah. 2008. “Weighted Least-Squares Method.” In The Concise Encyclopedia of Statistics, 566–69. New York, NY: Springer New York. https://doi.org/10.1007/978-0-387-32833-1_422.

Earlom, Richard. 1793. “Brook Taylor - National Portrait Gallery.” NPG D6930; Brook Taylor - Portrait - National Portrait Gallery. National Portrait Gallery. https://www.npg.org.uk/collections/search/portrait/mw40921/Brook-Taylor.

Fletcher, Roger. 1987. Practical Methods of Optimization. 2nd ed. New York: John Wiley & Sons.

Fox, John, and Sanford Weisberg. 2019. An R Companion to Applied Regression. Third. Thousand Oaks CA: Sage. https://www.john-fox.ca/Companion/.

François-Séraphin Delpech after a portrait by N. Maurin, Lithograph by. n.d. Portrait of Siméon-Denis Poisson. Courtesy of the Smithsonian Libraries and Archives. https://library.si.edu/image-gallery/74036.

Frick, Hannah, Fanny Chow, Max Kuhn, Michael Mahoney, Julia Silge, and Hadley Wickham. 2025. Rsample: General Resampling Infrastructure. https://doi.org/10.32614/CRAN.package.rsample.

Gelbart, Michael. 2017. “Data Science Terminology.” UBC MDS. Master of Data Science at the University of British Columbia. https://ubc-mds.github.io/resources_pages/terminology/.

Gelman, A., J. Hill, and A. Vehtari. 2021. Regression and Other Stories. Analytical Methods for Social Research. Cambridge University Press.

Gregory, James. 1668. Vera circuli et hyperbolae quadratura cui accedit geometria pars vniuersalis inseruiens quantitatum curuarum transmutationi & mensurae. Authore Iacobo Gregorio Abredonensi. Padua, Italy: Patavii: typis heredum Pauli Frambotti bibliop. https://archive.org/details/ita-bnc-mag-00001357-001/page/n10/mode/2up.

Harding, Edward. 1798. Portrait of Colin MacLaurin. Courtesy of the Smithsonian Libraries and Archives. https://library.si.edu/image-gallery/72863.

Harrell, Frank E. 2015. Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. 2nd ed. Cham: Springer. https://doi.org/10.1007/978-3-319-19425-7.

Harris, Charles R., K. Jarrod Millman, Stéfan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, Eric Wieser, et al. 2020. “Array Programming with NumPy.” Nature 585 (7825): 357–62. https://doi.org/10.1038/s41586-020-2649-2.

Hastie, Trevor, and Robert Tibshirani. 1986. “Generalized Additive Models.” Statistical Science 1 (3): 297–310. http://www.jstor.org/stable/2245459.

Hastie, Trevor, Robert Tibshirani, and Jerome Friedman. 2009. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. New York: Springer.

Hausman, Jerry, Bronwyn H. Hall, and Zvi Griliches. 1984. “Econometric Models for Count Data with an Application to the Patents-r & d Relationship.” Econometrica 52 (4): 909–38. http://www.jstor.org/stable/1911191.

Hernán, Miguel A. 2024. Causal Inference: What If. Edited by James M. Robins. Boca Raton.

Hu, Mei-Chen, Martina Pavlicova, and Edward V. Nunes. 2011. “Zero-Inflated and Hurdle Models of Count Data with Extra Zeros: Examples from an HIV-Risk Reduction Intervention Trial.” The American Journal of Drug and Alcohol Abuse 37 (5): 367–75. https://doi.org/10.3109/00952990.2011.597280.

Johnson, A. A., M. Q. Ott, and M. Dogucu. 2022. Bayes Rules!: An Introduction to Applied Bayesian Modeling. Chapman & Hall/CRC Texts in Statistical Science. CRC Press. https://www.bayesrulesbook.com/.

King, Gary. 1988. “Statistical Models for Political Science Event Counts: Bias in Conventional Procedures and Evidence for the Exponential Poisson Regression Model.” American Journal of Political Science 32 (3): 838–63. http://www.jstor.org/stable/2111248.

Kuhn, Max, and Kjell Johnson. 2013. Applied Predictive Modeling. New York: Springer. https://doi.org/10.1007/978-1-4614-6849-3.

Kullback, S., and R. A. Leibler. 1951. “On Information and Sufficiency.” The Annals of Mathematical Statistics 22 (1): 79–86. https://doi.org/10.1214/aoms/1177729694.

Kusuma, Rahmaniar Dwinta, and Yogo Purwono. 2019. “Zero-Inflated Poisson Regression Analysis on Frequency of Health Insurance Claim PT. XYZ.” In Proceedings of the 12th International Conference on Business and Management Research (ICBMR 2018), 72:321–25. Advances in Economics, Business and Management Research. Atlantis Press. https://doi.org/10.2991/icbmr-18.2019.52.

Lambert, Diane. 1992. “Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing.” Technometrics 34 (1): 1–14. https://doi.org/10.1080/00401706.1992.10485228.

Leemis, Larry. n.d. “Univariate Distribution Relationship Chart.” https://www.math.wm.edu/~leemis/chart/UDR/UDR.html.

Lilliefors, Hubert W. 1969. “On the Kolmogorov–Smirnov Test for the Exponential Distribution with Mean Unknown.” Journal of the American Statistical Association 64 (325): 387–89. https://doi.org/10.1080/01621459.1969.10500983.

Liu, Dong C., and Jorge Nocedal. 1989. “On the Limited Memory BFGS Method for Large Scale Optimization.” Mathematical Programming 45: 503–28. https://doi.org/10.1007/BF01589116.

Lohr, S. L. 2021. Sampling: Design and Analysis. Chapman; Hall/CRC. https://doi.org/10.1201/9780429298899.

Maclaurin, Colin. 1742. A Treatise of Fluxions. Edinburgh, Scotland: Printed for the Author by T.W.; T. Ruddimans. https://archive.org/details/treatiseonfluxio02macl/page/n5/mode/2up.

Maloney, Tom, Ryan Phelan, and Naira Simmons. 2018. “Saving the Horseshoe Crab: A Synthetic Alternative to Horseshoe Crab Blood for Endotoxin Detection.” PLOS Biology 16 (10): e2006607. https://doi.org/10.1371/journal.pbio.2006607.

McCullagh, Peter. 1980. “Regression Models for Ordinal Data.” Journal of the Royal Statistical Society: Series B (Methodological) 42 (2): 109–42. https://doi.org/10.1111/j.2517-6161.1980.tb01109.x.

Nelder, J. A., and R. W. M. Wedderburn. 1972. “Generalized Linear Models.” Journal of the Royal Statistical Society, Series a (General) 135 (3): 370–84.

Newton, Isaac, and John Colson. 1736. Methodus Fluxionum Et Serierum Infinitarum. London: Printed by Henry Woodfall;; sold by John Nourse. https://www.loc.gov/item/42048007/.

O’Donnell, T. 1936. History of Life Insurance in Its Formative Years. Compiled from Approved Sources by T. O’Donnell. Chicago.

Pedregosa, F., G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, et al. 2011. “Scikit-Learn: Machine Learning in Python.” Journal of Machine Learning Research 12: 2825–30.

Poisson, Siméon-Denis. 1837. Recherches Sur La Probabilité Des Jugements En Matière Criminelle Et En Matière Civile, Précédées Des règles générales Du Calcul Des Probabilités. Paris: Bachelier.

R Core Team. 2024. “R: A Language and Environment for Statistical Computing.” Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Raphson, Joseph. 1697. Analysis Æquationum Universalis. 2nd ed. London: Thomas Bradyll. https://doi.org/10.3931/e-rara-13516.

Reinhart, Alex. 2015. Statistics Done Wrong: The Woefully Complete Guide. 1st ed. San Francisco, CA: No Starch Press. https://www.statisticsdonewrong.com/index.html.

Robinson, David, Alex Hayes, and Simon Couch. 2025. Broom: Convert Statistical Objects into Tidy Tibbles. https://broom.tidymodels.org/.

Rousseeuw, Peter J., and Annick M. Leroy. 1987. Robust Regression and Outlier Detection. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons. https://doi.org/10.1002/0471725382.

Scotland, National Galleries of. n.d. Professor James Gregory, 1638 - 1675 (1). Mathematician. Professor James Gregory, 1638 - 1675 (1). Mathematician | National Galleries. https://www.nationalgalleries.org/art-and-artists/31132/professor-james-gregory-1638-1675-mathematician.

Seabold, Skipper, and Josef Perktold. 2010. “Statsmodels: Econometric and Statistical Modeling with Python.” In 9th Python in Science Conference.

Shankar, Venkataraman, Fred Mannering, and Woodrow Barfield. 1995. “Effect of Roadway Geometrics and Environmental Factors on Rural Freeway Accident Frequencies.” Accident Analysis & Prevention 27 (3): 371–89. https://doi.org/10.1016/0001-4575(94)00078-Z.

Soch, Joram, The Book of Statistical Proofs, Maja, Pietro Monticone, Thomas J. Faulkenberry, Alex Kipnis, Kenneth Petrykowski, et al. 2024. “StatProofBook/StatProofBook.github.io: StatProofBook 2023.” Zenodo. https://doi.org/10.5281/zenodo.10495684.

Stephens, Michael A. 1974. “EDF Statistics for Goodness of Fit and Some Comparisons.” Journal of the American Statistical Association 69 (347): 730–37. https://doi.org/10.2307/2286009.

Tai, Man-Yeung (Andy). 2026. “Zero-Inflated Poisson Auto Insurance Claims Data.” Regression Cookbook GitHub repository. https://github.com/andytai7/cookbook/blob/main/raw-data/zero_inflated_poisson.csv.

Taylor, Brook. 1715. Methodus incrementorum directa & inversa. Auctore Brook Taylor, LL. D. & Regiae Societatis Secretario. London, England: Typis Pearsonianis Prostant apud Gul. Innys ad Insignia Principis in Coemeterio Paulino MDCCXV. https://archive.org/details/bim_eighteenth-century_methodus-incrementorum-d_taylor-brook_1717.

The Pandas Development Team. 2024. “Pandas-Dev/Pandas: Pandas.” Zenodo. https://doi.org/10.5281/zenodo.3509134.

Tuenter, H. J. H. 2000. “On the Generalized Poisson Distribution.” Statistica Neerlandica 54 (3): 374–76. https://doi.org/10.1111/1467-9574.00147.

Ushey, Kevin, JJ Allaire, and Yuan Tang. 2025. Reticulate: Interface to ’Python’. https://doi.org/10.32614/CRAN.package.reticulate.

Van Rossum, Guido, and Fred L. Drake. 2009. Python 3 Reference Manual. Scotts Valley, CA: CreateSpace.

Virtanen, Pauli, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, et al. 2020. “SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python.” Nature Methods 17: 261–72. https://doi.org/10.1038/s41592-019-0686-2.

Wasserman, Larry. 2004. All of Statistics: A Concise Course in Statistical Inference. New York: Springer. https://doi.org/10.1007/978-0-387-21736-9.

Weisstein, Eric W. n.d.a. “Gamma Function.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/GammaFunction.html.

———. n.d.b. “Taylor Series.” From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/TaylorSeries.html.

Wickham, Hadley, Mara Averick, Jennifer Bryan, Winston Chang, Lucy D’Agostino McGowan, Romain François, Garrett Grolemund, et al. 2019. “Welcome to the tidyverse.” Journal of Open Source Software 4 (43): 1686. https://doi.org/10.21105/joss.01686.

Wickham, Hadley, Romain François, Lionel Henry, Kirill Müller, and Davis Vaughan. 2023. Dplyr: A Grammar of Data Manipulation. https://dplyr.tidyverse.org.

Winkelmann, Rainer. 2004. “Health Care Reform and the Number of Doctor Visits—an Econometric Analysis.” Journal of Applied Econometrics 19 (4): 455–72. https://doi.org/10.1002/jae.764.

Wu, Lang. 2009. Mixed Effects Models for Complex Data. 1st ed. Chapman; Hall/CRC. https://doi.org/10.1201/9781420074086.

Zeileis, Achim, and Torsten Hothorn. 2002. “Diagnostic Checking in Regression Relationships.” R News 2 (3): 7–10. https://CRAN.R-project.org/doc/Rnews/.