The Zero, One and Zero-and-one-inflated New unit-Lindley Distributions
Conteúdo do artigo principal
Resumo
Neste artigo propomos as distribuições New unit-Lindley inflacionada em zero, em um e em zero e um como extensões naturais da distribuição New unit-Lindley para modelar respostas contínuas medidas nos intervalos $[0,1)$, $(0,1]$ e $[0,1]$. Estas distribuições foram construídas a partir de combinações convexas entre a distribuição New unit-Lindley e as distribuições degenerada em zero, em um e Bernoulli. Elas também contam com uma série de propriedades interessantes tais como serem membros da família exponencial além de contar com formas as funções de distribuição acumulada, quantil e para os momentos. Aspectos inferenciais e estruturas de regressão são discutidas neste trabalho bem como um estudo de simulação Monte Carlo para avaliar a performance dos coeficientes regressores. Por fim, trazemos uma aplicação a dados reais sobre a taxa de suicídio no ano de 2016.
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Referências
ABRAMOWITZ, M.; STEGUN, I. A. Handbook of mathematical functions with formulas, graphs, and mathematical tables. New York: United States Department of Commerce, National Bureau of Standards, 1974
BAPAT, S. R.; BHARDWAJ, R. On an Inflated Unit-Lindley Distribution. arXivpreprint arXiv:2102.04687, 2021.
CASELLA, G.; BERGER, R. L. Statistical inference. Califórnia: Duxbury Pacific Grove, 2002. v. 2.
CHAI, H. et al. A marginalized two-part beta regression model for microbiome compositional data. PLoS computational biology, v. 14, n. 7, p. e1006329, 2018.
CORLESS, R. M. et al. On the Lambert W function. Advances in Computational Mathematics, v. 5, n. 1, p. 329–359, 1996.
CRIBARI-NETO, F.; SANTOS, J. Inflated Kumaraswamy distributions. Anais da Academia Brasileira de Ciências, v. 91, n. 2, 2019.
ENEA, M. et al.gamlss.inf: Fitting Mixed (Inflated and Adjusted) Distributions. [S.l.], 2019. R package version 1.0-1. Disponível em: <https://CRAN.R-project.org/package=gamlss.inf>.
GHITANY, M. E. et al. The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval. Communications in Statistics-Theory and Methods, v. 48, n. 14, p. 3423–3438, 2019.
JODRÁ, P. Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function. Mathematics and Computers inSimulation, v. 81, n. 4, p. 851–859, 2010.
LINDLEY, D. V. Fiducial distributions and bayes’ theorem. Journal of the RoyalStatistical Society: Series B (Methodological), v. 20, n. 1, p. 102–107, 1958.
LIU, P. et al. Zero-one-inflated simplex regression models for the analysis of continuous proportion data. Statistics and Its Interface, v. 13, n. 2, p. 193–208,2020.
MAZUCHELI, J.; BAPAT, S. R.; MENEZES, A. F. B. A new one-parameter unit-lindley distribution.Chilean Journal of Statistics (ChJS), v. 11, n. 1, 2020.
MAZUCHELI, J.; MENEZES, A. F. B.; CHAKRABORTY, S. On the one parameter unit-Lindley distribution and its associated regression model for proportion data. Journal of Applied Statistics, v. 46, n. 4, p. 700–714, 2019.
MAZUCHELI, J.; MENEZES, A. F. B.; DEY, S. Unit-Gompertz distribution with applications. Statistica, v. 79, n. 1, p. 25–43, 2019.
MAZUCHELI, J.; MENEZES, A. F. B.; GHITANY, M. E. The unit-Weibulldistribution and associated inference. Journal of Applied Probability and Statistics, v. 13, p. 1–22, 2018
MENEZES, A. F.; MAZUCHELI, J.; BOURGUIGNON, M. A parametric quantile regression approach for modelling zero-or-one inflated double bounded data. Biometrical Journal, v. 63, n. 4, p. 841–858, 2021.
NELDER, J. A.; WEDDERBURN, R. W. Generalized linear models. Journal of the Royal Statistical Society: Series A (General), Wiley Online Library, v. 135, n. 3, p.370–384, 1972.
OSPINA, R.; FERRARI, S. L. A general class of zero-or-one inflated beta regression models. Computational Statistics & Data Analysis, v. 56, n. 6, p. 1609–1623, 2012.
OSPINA, R.; FERRARI, S. L. P. Inflated beta distributions. Statistical Papers, v. 51, n. 1, p. 111, 2010.
QUEIROZ, F. F.; LEMONTE, A. J. A broad class of zero-or-one inflated regression models for rates and proportions. Canadian Journal of Statistics, v. 49, n. 2, p.566–590, 2021.R Core Team.R: A Language and Environment for Statistical Computing. Vienna, Austria, 2019. Disponível em: <https://www.R-project.org/>.
RIGBY, R. A.; STASINOPOULOS, D. M. Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society: Series C (AppliedStatistics), v. 54, n. 3, p. 507–554, 2005.
RIVAS, L.; CAMPOS, F. Zero inflated waring distribution. Communications inStatistics-Simulation and Computation, p. 1–16, 2021.
SANTOS, B.; BOLFARINE, H. Bayesian analysis for zero-or-one inflated proportion data using quantile regression. Journal of Statistical Computation and Simulation, v. 85, n. 17, p. 3579–3593, 2015.
SANTOS, B.; BOLFARINE, H. Bayesian quantile regression analysis for continuous data with a discrete component at zero. Statistical Modelling, v. 18, n. 1, p. 73–93,2018.
SILVA, A. R. et al. Augmented-limited regression models with an application to the study of the risk perceived using continuous scales. Journal of Applied Statistics, v. 48, n. 11, p. 1998–2021, 2021.
TOMARCHIO, S. D.; PUNZO, A. Modelling the loss given default distribution via a family of zero-and-one inflated mixture models. Journal of the Royal Statistical Society: Series A (Statistics in Society), v. 182, n. 4, p. 1247–1266, 2019.
XIE, M.; HE, B.; GOH, T. Zero-inflated poisson model in statistical process control. Computational Statistics & data Analysis, v. 38, n. 2, p. 191–201, 2001.