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Communications in Statistics - Theory and Methods Volume 20, 1991 - Issue 10
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Original Articles

Goodness of fit for the poisson distribution based on the probability generating function

R. Rueda $sup:1$esup IIMAS, UN AM, UN AM Apartado Postal 20-726, Mexico, D.F, 01000
,
F. O' Reilly $sup:1$esup IIMAS, UN AM, UN AM Apartado Postal 20-726, Mexico, D.F, 01000
&
V. Pé rez- Abreu $sup:2$esup CIM.AT, Apartado Postal 402, Guanajuato, Gto
Pages 3093-3110 | Received 01 Jun 1990, Published online: 27 Jun 2007

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Antonio Di Noia, Lucio Barabesi, Marzia Marcheselli, Caterina Pisani & Luca Pratelli. (2023) Goodness-of-fit test for count distributions with finite second moment. Journal of Nonparametric Statistics 35:1, pages 19-37.
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S. Y. Tay, C. M. Ng & S. H. Ong. (2019) Parameter estimation by minimizing a probability generating function-based power divergence. Communications in Statistics - Simulation and Computation 48:10, pages 2898-2912.
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Maryam Sharifdoust, Choung Min Ng & Seng-Huat Ong. (2016) Probability Generating Function Based Jeffrey's Divergence for Statistical Inference. Communications in Statistics - Simulation and Computation 45:7, pages 2445-2458.
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P. Prajitha. (2015) Modeling of Discrete HNBUE Class with Hypothesis Testing Application. Communications in Statistics - Simulation and Computation 44:7, pages 1867-1878.
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Simos G. Meintanis, Ma Dolores JimÉnez Gamero & V. Alba-fernÁndez. (2014) A Class of Goodness-of-fit Tests Based on Transformation. Communications in Statistics - Theory and Methods 43:8, pages 1708-1735.
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S. Z. Sim & S. H. Ong. (2010) Parameter Estimation for Discrete Distributions by Generalized Hellinger-Type Divergence Based on Probability Generating Function. Communications in Statistics - Simulation and Computation 39:2, pages 305-314.
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R. Rueda & F. O’ Reilly. (1999) Tests of fit for discrete distributions based on the probability generating function. Communications in Statistics - Simulation and Computation 28:1, pages 259-274.
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Mary M. Dowling & Miguel Nakamura. (1997) Estimating parameters for discrete distributions via the empirical probability generating function. Communications in Statistics - Simulation and Computation 26:1, pages 301-313.
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Norbert Henze & Bernhard Klar. (1995) Bootstrap based goodness of fit tests for the generalized poisson model. Communications in Statistics - Theory and Methods 24:7, pages 1875-1896.
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T.W. Epps. (1995) A test of fit for lattice distributions. Communications in Statistics - Theory and Methods 24:6, pages 1455-1479.
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Miguel Nakamura & Victor Pérez-Abreu. (1993) Exploratory data analysis for counts using the empirical probability generating function . Communications in Statistics - Theory and Methods 22:3, pages 827-842.
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Yeh-Ching Low, Yook-Ngor Phang, Wooi-Chen Khoo & Seng-Huat Ong. Parameter estimation for strict arcsine distribution. Communications in Statistics - Simulation and Computation 0:0, pages 1-10.
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Articles from other publishers (22)

Rasmus Erlemann & Bo Henry Lindqvist. (2022) Conditional Goodness-of-Fit Tests for Discrete Distributions. Journal of Statistical Theory and Practice 16:1.
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Steffen Betsch, Bruno Ebner & Franz Nestmann. (2022) Characterizations of non-normalized discrete probability distributions and their application in statistics. Electronic Journal of Statistics 16:1.
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P.A. Mijburgh & I.J.H. Visagie. (2020) An overview of goodness-of-fit tests for the Poisson distribution. South African Statistical Journal 54:2, pages 207-230.
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Apostolos Batsidis, María Dolores Jiménez-Gamero & Artur J. Lemonte. (2019) On goodness-of-fit tests for the Bell distribution. Metrika 83:3, pages 297-319.
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Šárka Hudecová, Marie Hušková & Simos G. Meintanis. (2017) Tests for Structural Changes in Time Series of Counts. Scandinavian Journal of Statistics 44:4, pages 843-865.
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L. Baringhaus, B. Ebner & N. Henze. (2016) The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications. Annals of the Institute of Statistical Mathematics 69:5, pages 969-995.
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M. D. Jiménez-Gamero & A. Batsidis. (2017) Minimum distance estimators for count data based on the probability generating function with applications. Metrika 80:5, pages 503-545.
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M.D. Jiménez-Gamero, M.V. Alba-Fernández, P. Jodrá & I. Barranco-Chamorro. (2015) An approximation to the null distribution of a class of Cramér–von Mises statistics. Mathematics and Computers in Simulation 118, pages 258-272.
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F. Novoa-Muñoz & M. D. Jiménez-Gamero. (2013) Testing for the bivariate Poisson distribution. Metrika 77:6, pages 771-793.
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Jin Seo Cho & Halbert White. (2011) Generalized runs tests for the IID hypothesis. Journal of Econometrics 162:2, pages 326-344.
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M. L. Esquível. (2008) Probability Generating Functions for Discrete Real-Valued Random Variables. Theory of Probability & Its Applications 52:1, pages 40-57.
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Gábor Szűcs. (2007) Parametric bootstrap tests for continuous and discrete distributions. Metrika 67:1, pages 63-81.
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Simos Meintanis & Jan Swanepoel. (2007) Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms. Statistics & Probability Letters 77:10, pages 1004-1013.
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Manuel Leote Tavares Ingles Esquivel & Manuel Leote Tavares Ingles Esquivel. (2007) Probability generating functions for discrete real-valued random variablesProbability generating functions for discrete real-valued random variables. Теория вероятностей и ее применения Teoriya Veroyatnostei i ee Primeneniya 52:1, pages 129-149.
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Simos G. Meintanis. (2007) A new goodness-of-fit test for certain bivariate distributions applicable to traffic accidents. Statistical Methodology 4:1, pages 22-34.
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José M. González-Barrios, Federico O’Reilly & Raúl Rueda. (2006) Goodness of Fit for Discrete Random Variables Using the Conditional Density. Metrika 64:1, pages 77-94.
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Gábor Szűcs. (2005) Approximations of empirical probability generating processes. Statistics & Risk Modeling 23:1, pages 67-80.
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Nora Gürtler & Norbert Henze. (2000) Recent and classical goodness-of-fit tests for the Poisson distribution. Journal of Statistical Planning and Inference 90:2, pages 207-225.
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John J. Spinelli & Michael A. Stephens. (2008) Cramér‐von Mises tests of fit for the Poisson distribution. Canadian Journal of Statistics 25:2, pages 257-268.
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Norbert Henze. (2008) Empirical‐distribution‐function goodness‐of‐fit tests for discrete models. Canadian Journal of Statistics 24:1, pages 81-93.
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Miguel Nakamura & Victor PÉrez-Abreu. (1993) Use of an empirical probability generating function for testing a Poisson model. Canadian Journal of Statistics 21:2, pages 149-156.
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Miguel Nakamura & Víctor Pérez-Abreu. (1993) Empirical probability generating function. Insurance: Mathematics and Economics 12:3, pages 287-295.
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