{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T09:10:02Z","timestamp":1758705002104,"version":"3.44.0"},"publisher-location":"Cham","reference-count":48,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031689482"},{"type":"electronic","value":"9783031689499"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-68949-9_27","type":"book-chapter","created":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T17:59:02Z","timestamp":1736531942000},"page":"363-379","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Count Models and Randomness Patterns"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3364-0357","authenticated-orcid":false,"given":"Sandra","family":"Mendon\u00e7a","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8999-1354","authenticated-orcid":false,"given":"Dinis","family":"Pestana","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,11]]},"reference":[{"key":"27_CR1","volume-title":"Distributions in Statistics: Discrete Distributions","author":"NL Johnson","year":"1969","unstructured":"Johnson, N.L., Kotz, S.: Distributions in Statistics: Discrete Distributions. Houghton Mifflin, Boston (1969)"},{"key":"27_CR2","volume-title":"Urn Models and Their Application: An Approach to Modern Discrete Probability Theory","author":"NL Johnson","year":"1977","unstructured":"Johnson, N.L., Kotz, S.: Urn Models and Their Application: An Approach to Modern Discrete Probability Theory. Wiley, Hoboken (1977)"},{"key":"27_CR3","unstructured":"Patil, G., Boswell, M., Joshi, S., Ratnaparkhi, M.: Dictionary and Bibliography of Statistical Distributions in Scientific Work,Vol. I: Discrete Models. International Co-Operative Publishing House, Fairland (1984)"},{"key":"27_CR4","doi-asserted-by":"crossref","unstructured":"Johnson, N.L., Kemp, A.W., Kotz, S.: Univariate Discrete Distributions. Wiley, Hoboken (2005). https:\/\/doi.org\/10.1002\/0471715816","DOI":"10.1002\/0471715816"},{"issue":"1","key":"27_CR5","first-page":"127","volume":"54","author":"G Shmueli","year":"2005","unstructured":"Shmueli, G., Minka, T.P., Kadane, J.B., Borle, S., Boatwright, P.: A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Appl. Stat. 54(1), 127\u2013142 (2005). https:\/\/doi.org\/10.1111\/j.1467-9876.2005.00474.x","journal-title":"Appl. Stat."},{"key":"27_CR6","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1186\/s40488-017-0077-0","volume":"4","author":"KF Sellers","year":"2017","unstructured":"Sellers, K.F., Swift, A.W., Weems, K.S.: A flexible distribution class for count data. J. Stat. Distrib. Appl. 4, 22 (2017). https:\/\/doi.org\/10.1186\/s40488-017-0077-0","journal-title":"J. Stat. Distrib. Appl."},{"issue":"1","key":"27_CR7","doi-asserted-by":"publisher","first-page":"9","DOI":"10.3390\/econometrics8010009","volume":"8","author":"BP McCabe","year":"2020","unstructured":"McCabe, B.P., Skeels, C.L.: Distributions you can count on \u2026but what\u2019s the point? Econometrics 8(1), 9 (2020). https:\/\/doi.org\/10.3390\/econometrics8010009","journal-title":"Econometrics"},{"key":"27_CR8","unstructured":"Katz, L.: Characteristics of frequency functions defined by first order difference equations. Ph.D. Thesis, University of Michigan (1945). PhD thesis"},{"key":"27_CR9","first-page":"175","volume-title":"Classical and Contagious Discrete Distributions","author":"L Katz","year":"1965","unstructured":"Katz, L.: Unified treatment of a broad class of discrete probability distributions. In: G.P. Patil (ed.) Classical and Contagious Discrete Distributions, pp. 175\u2013182. Pergamon, Oxford (1965)"},{"key":"27_CR10","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1098\/rsta.1895.0010","volume":"186","author":"K Pearson","year":"1895","unstructured":"Pearson, K.: Contributions to the mathematical theory of evolution II. Skew variation in homogeneous material. Philos. Trans. R. Soc. Lond. A 186, 343\u2013414 (1895). http:\/\/www.jstor.org\/stable\/90649","journal-title":"Skew variation in homogeneous material. Philos. Trans. R. Soc. Lond. A"},{"key":"27_CR11","volume-title":"Frequency Curves and Correlation","author":"WP Elderton","year":"1938","unstructured":"Elderton, W.P.: Frequency Curves and Correlation. Cambridge University Press, Cambridge (1938)"},{"issue":"1","key":"27_CR12","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1017\/S0515036100006796","volume":"12","author":"HH Panjer","year":"1981","unstructured":"Panjer, H.H.: Recursive evaluation of a family of compound distributions. ASTIN Bullet. 12(1), 22\u201326 (1981)","journal-title":"ASTIN Bullet."},{"key":"27_CR13","volume-title":"Loss Models: From Data to Decisions","author":"SA Klugman","year":"1998","unstructured":"Klugman, S.A., Panjer, H.H., Willmot, G.E.: Loss Models: From Data to Decisions. Wiley, Hoboken (1998)"},{"key":"27_CR14","doi-asserted-by":"publisher","DOI":"10.1002\/9780470317044","volume-title":"Stochastic Processes for Insurance and Finance","author":"T R\u00f3lski","year":"1999","unstructured":"R\u00f3lski, T., Schmidli, H., Schmidt, V., Teugels, J.: Stochastic Processes for Insurance and Finance. Wiley, Hoboken (1999)"},{"issue":"1","key":"27_CR15","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1017\/S0515036100006802","volume":"12","author":"B Sundt","year":"1981","unstructured":"Sundt, B., Jewell, W.S.: Further results on recursive evaluation of compound distributions. ASTIN Bullet. 12(1), 27\u201339 (1981). https:\/\/doi.org\/10.1017\/S0515036100006802","journal-title":"ASTIN Bullet."},{"issue":"1","key":"27_CR16","doi-asserted-by":"publisher","first-page":"17","DOI":"10.2143\/AST.18.1.2014957","volume":"18","author":"GE Willmot","year":"1987","unstructured":"Willmot, G.E.: Sundt and Jewell\u2019s family of discrete distributions. ASTIN Bullet. 18(1), 17\u201329 (1987). https:\/\/doi.org\/10.2143\/AST.18.1.2014957","journal-title":"ASTIN Bullet."},{"issue":"2","key":"27_CR17","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1093\/biomet\/61.2.263","volume":"61","author":"S Engen","year":"1974","unstructured":"Engen, S.: On species frequency models. Biometrika 61(2), 263\u2013270 (1974). https:\/\/doi.org\/10.1093\/biomet\/61.2.263","journal-title":"Biometrika"},{"key":"27_CR18","doi-asserted-by":"publisher","first-page":"283","DOI":"10.2143\/AST.32.2.1030","volume":"32","author":"KT Hess","year":"2002","unstructured":"Hess, K.T., Liewald, A., Schmidt, K.D.: An extension of Panjer\u2019s recursion. ASTIN Bullet. 32, 283\u2013297 (2002)","journal-title":"ASTIN Bullet."},{"issue":"2","key":"27_CR19","doi-asserted-by":"publisher","first-page":"145","DOI":"10.57805\/revstat.v2i2.12","volume":"2","author":"D Pestana","year":"2004","unstructured":"Pestana, D., Velosa, S.: Extensions of Katz-Panjer families of discrete distributions. REVSTAT \u2013 Stat. J. 2(2), 145\u2013162 (2004). https:\/\/doi.org\/10.57805\/revstat.v2i2.12","journal-title":"REVSTAT \u2013 Stat. J."},{"issue":"1","key":"27_CR20","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1017\/S0305004100023185","volume":"43","author":"MCK Tweedie","year":"1947","unstructured":"Tweedie, M.C.K.: Functions of a statistical variate with given means, with special reference to Laplacian distributions. Proc. Cambridge Math. Soc. 43(1), 41\u201349 (1947). https:\/\/doi.org\/10.1017\/S0305004100023185","journal-title":"Proc. Cambridge Math. Soc."},{"issue":"1","key":"27_CR21","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1214\/aoms\/1177729894","volume":"21","author":"A Noack","year":"1950","unstructured":"Noack, A.: A class of random variables with discrete distributions. Ann. Math. Stat. 21(1), 127\u2013132 (1950). https:\/\/doi.org\/10.1214\/aoms\/1177729894","journal-title":"Ann. Math. Stat."},{"key":"27_CR22","first-page":"109","volume":"15","author":"DD Kosambi","year":"1949","unstructured":"Kosambi, D.D.: Characteristic properties of series distributions. Proc. Natl. Inst. Sci. India 15, 109\u2013113 (1949)","journal-title":"Proc. Natl. Inst. Sci. India"},{"key":"27_CR23","unstructured":"Kemp, A.W.: A wide class of discrete distributions and the associated differential equations. Sankhy\u0101 Indian J. Stat. A (1961\u20132002) 30(4), 401\u2013410 (1968). http:\/\/www.jstor.org\/stable\/25049542"},{"key":"27_CR24","doi-asserted-by":"publisher","first-page":"2969","DOI":"10.1007\/s00362-021-01222-7","volume":"62","author":"D Cahoy","year":"2021","unstructured":"Cahoy, D., Di Nardo, E., Polito, F.: Flexible models for overdispersed and underdispersed count data. Stat. Pap. 62, 2969\u20132990 (2021). https:\/\/doi.org\/10.1007\/s00362-021-01222-7","journal-title":"Stat. Pap."},{"key":"27_CR25","doi-asserted-by":"crossref","unstructured":"Gani, J.: The Craft of Probabilistic Modelling: A Collection of Personal Accounts. Springer, New York (1986). https:\/\/doi.org\/10.1007\/978-1-4613-8631-5","DOI":"10.1007\/978-1-4613-8631-5"},{"issue":"2","key":"27_CR26","doi-asserted-by":"publisher","first-page":"194","DOI":"10.3390\/fractalfract7020194","volume":"7","author":"MF Brilhante","year":"2023","unstructured":"Brilhante, M.F., Gomes, M.I., Mendon\u00e7a, S., Pestana, D., Pestana, P.: Generalized Beta models and population growth: so many routes to chaos. Fract. Fractional 7(2), 194 (2023). https:\/\/doi.org\/10.3390\/fractalfract7020194","journal-title":"Fract. Fractional"},{"key":"27_CR27","doi-asserted-by":"crossref","unstructured":"Brilhante, M.F., Pestana, P.: BetaBoop function, BetaBoop random variables and extremal population growth. In: M. Lovric (ed.) International Encyclopedia of Statistical Science. Springer, Berlin, Germany, 2nd edition (2024). In press.","DOI":"10.1007\/978-3-662-69359-9_66"},{"key":"27_CR28","volume-title":"Table of Integrals, Series, and Products","author":"R Gradshteyn","year":"2007","unstructured":"Gradshteyn, R.: Table of Integrals, Series, and Products. Elsevier, Amsterdam (2007)"},{"key":"27_CR29","doi-asserted-by":"publisher","unstructured":"i Cancho, R.F., Sol\u00e9, R.V.: Least effort and the origins of scaling in human language. Proc. Natl. Acad. Sci. USA 100(3), 788\u2013791 (2003). https:\/\/doi.org\/10.1073\/pnas.0335980100","DOI":"10.1073\/pnas.0335980100"},{"issue":"2\u20133","key":"27_CR30","first-page":"177","volume":"13","author":"A Eftekhari","year":"2011","unstructured":"Eftekhari, A.: Fractal geometry of texts: an initial application to the works of Shakespeare. J. Quant. Ling. 13(2\u20133), 177\u2013193 (2011). https:\/\/doi.org\/10.1080\/09296170600850106","journal-title":"J. Quant. Ling."},{"key":"27_CR31","unstructured":"Martins, N.S., Gomes, D., Dias, E.: O L\u00e9xico de Guimar\u00e3es Rosa. Edusp, S\u00e3o Paulo (2001)"},{"key":"27_CR32","volume-title":"Matem\u00e1tica B\u00e1sica, Parte 07","author":"HJ Bortolossi","year":"2018","unstructured":"Bortolossi, H.J.: Matem\u00e1tica B\u00e1sica, Parte 07. Universidade Federal Fluminense, Rio de Janeiro, Brazil (2018)"},{"key":"27_CR33","first-page":"81","volume":"42","author":"TA Marques","year":"2005","unstructured":"Marques, T.A., Pestana, D., Velosa, S.: Count data models in Biometry and randomness patterns in birds extra-pair paternity. Biomet. Lett. 42, 81\u2013112 (2005). https:\/\/sparrow.up.poznan.pl\/biometrical.letters\/full\/BL%2042%202%201.pdf","journal-title":"Biomet. Lett."},{"issue":"6","key":"27_CR34","doi-asserted-by":"publisher","first-page":"1842","DOI":"10.1109\/18.165464","volume":"38","author":"W Li","year":"1992","unstructured":"Li, W.: Random texts exhibit Zipf\u2019s-law-like word frequency distribution. IEEE Trans. Inf. Theory 38(6), 1842\u20131845 (1992). https:\/\/doi.org\/10.1109\/18.165464","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"27_CR35","first-page":"1","volume":"2","author":"S Chakraborty","year":"2015","unstructured":"Chakraborty, S.: Generating discrete analogues of continuous probability distributions \u2014 a survey of methods and constructions. J. Stat. Distrib. Appl. 2(6), 1\u201330 (2015). https:\/\/doi.org\/10.1186\/s40488-015-0028-6","journal-title":"J. Stat. Distrib. Appl."},{"key":"27_CR36","first-page":"310","volume":"73","author":"V Belevitch","year":"1959","unstructured":"Belevitch, V.: On the statistical laws of linguistic distributions. Ann. Soc. Sci. Bruxelles 73, 310\u2013326 (1959). http:\/\/www.csl.sri.com\/users\/neumann\/belevitch.pdf","journal-title":"Ann. Soc. Sci. Bruxelles"},{"key":"27_CR37","unstructured":"Kapur, J.N.: Maximum-Entropy Models in Science and Engineering. Wiley Eastern Limited, New Delhi (1989)"},{"key":"27_CR38","doi-asserted-by":"publisher","first-page":"942","DOI":"10.3390\/stats6030059","volume":"6","author":"SH Ong","year":"2023","unstructured":"Ong, S.H., Sim, S.Z., Liu, S., Srivastava, H.M.: A family of finite mixture distributions for modelling dispersion in count data. Stats 6, 942\u2013955 (2023). https:\/\/doi.org\/10.3390\/stats6030059","journal-title":"Stats"},{"issue":"4","key":"27_CR39","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1007\/s11464-018-0714-z","volume":"13","author":"H Zhang","year":"2018","unstructured":"Zhang, H., Tan, K., Li, B.: COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data. Front. Math. China 13(4), 967\u2013998 (2018). https:\/\/doi.org\/10.1007\/s11464-018-0714-z","journal-title":"Front. Math. China"},{"issue":"339","key":"27_CR40","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1080\/01621459.1972.10481254","volume":"67","author":"WJ Conover","year":"1972","unstructured":"Conover, W.J.: A Kolmogorov goodness-of-fit test for discontinuous distributions. J. Am. Stat. Assoc. 67(339), 591\u2013596 (1972). https:\/\/doi.org\/10.1080\/01621459.1972.10481254","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"27_CR41","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1002\/cjs.5550350111","volume":"35","author":"RA Lockhart","year":"2007","unstructured":"Lockhart, R.A., Spinelli, J.J., Stephens, M.A.: Cram\u00e9r\u2013von Mises statistics for discrete distributions with unknown parameters. Can. J. Stat. La Revue Can. Stat. 35(1), 125\u2013133 (2007). https:\/\/doi.org\/10.1002\/cjs.5550350111","journal-title":"Can. J. Stat. La Revue Can. Stat."},{"issue":"2","key":"27_CR42","doi-asserted-by":"publisher","first-page":"207","DOI":"10.37920\/sasj.2020.54.2.6","volume":"54","author":"PA Mijburgh","year":"2020","unstructured":"Mijburgh, P.A., Visagie, I.J.H.: An overview of goodness-of-fit tests for the Poisson distribution. South Afr. Stat. J. 54(2), 207\u2013230 (2020). https:\/\/doi.org\/10.37920\/sasj.2020.54.2","journal-title":"South Afr. Stat. J."},{"key":"27_CR43","unstructured":"Zeimbekakis, A.: On misuses of the Kolmogorov\u2013Smirnov test for one-sample goodness-of-fit. Honors Scholar Theses 894 (2022). https:\/\/opencommons.uconn.edu\/srhonors_theses\/894"},{"issue":"1","key":"27_CR44","first-page":"63","volume":"66","author":"GJ Babu","year":"2004","unstructured":"Babu, G.J., Rao, C.R.: Goodness-of-fit tests when parameters are estimated. Sankhy\u0101 66(1), 63\u201374 (2004). http:\/\/www.jstor.org\/stable\/25053332","journal-title":"Sankhy\u0101"},{"issue":"5","key":"27_CR45","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1214\/aop\/1176994950","volume":"7","author":"FW Steutel","year":"1979","unstructured":"Steutel, F.W., van Harn, K.: Discrete analogues of self-decomposability and stability. Ann. Probabil. 7(5), 893\u2013899 (1979). https:\/\/doi.org\/10.1214\/aop\/1176994950","journal-title":"Ann. Probabil."},{"issue":"4","key":"27_CR46","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1080\/03610929608831728","volume":"25","author":"AO Hall","year":"1996","unstructured":"Hall, A.O.: Maximum term of a particular autoregressive sequence with discrete margins. Commun. Stat. Theory Methods 25(4), 721\u2013736 (1996). https:\/\/doi.org\/10.1080\/03610929608831728","journal-title":"Commun. Stat. Theory Methods"},{"issue":"1","key":"27_CR47","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1214\/aos\/1176345690","volume":"10","author":"CN Morris","year":"1982","unstructured":"Morris, C.N.: Natural exponential families with quadratic variance functions. Ann. Stat. 10(1), 65\u201380 (1982)","journal-title":"Ann. Stat."},{"key":"27_CR48","doi-asserted-by":"publisher","first-page":"343","DOI":"10.2991\/jsta.d.191105.001","volume":"18","author":"G Barmalzan","year":"2019","unstructured":"Barmalzan, G., Saboori, H., Kosari, S.: A modified negative binomial distribution: properties, overdispersion and underdispersion. J. Stat. Theory Appl. 18, 343\u2013350 (2019). https:\/\/doi.org\/10.2991\/jsta.d.191105.001","journal-title":"J. Stat. Theory Appl."}],"container-title":["Springer Proceedings in Mathematics &amp; Statistics","New Frontiers in Statistics and Data Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-68949-9_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T16:23:06Z","timestamp":1758644586000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-68949-9_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031689482","9783031689499"],"references-count":48,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-68949-9_27","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"11 January 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SPE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Congress of the Portuguese Statistical Society","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Evora","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 October 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 October 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"spe2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.spe2021.uevora.pt\/en\/inicio-english\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}