On the one parameter unit-Lindley distribution and its associated regression model for proportion data

References

• M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions with Formulas, graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, Dover Publications, Incorporated, New York, 1974.
   Google Scholar
• E. Cepeda-Cuervo, Variability modeling in generalized linear models, Ph.D. diss., Mathematics Institute, Universidade Federal do Rio de Janeiro, 2001.
   Google Scholar
• D.O. Cook, R. Kieschnick, and B. McCullough, Regression analysis of proportions in finance with self selection, J. Empir. Financ. 15 (2008), pp. 860–867. doi: 10.1016/j.jempfin.2008.02.001
   Web of Science ®Google Scholar
• R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, and D.E. Knuth, On the LambertW function, Adv. Comput. Math. 5 (1996), pp. 329–359. doi: 10.1007/BF02124750
   Web of Science ®Google Scholar
• D.R. Cox and E.J. Snell, A general definition of residuals, J. R. Stat. Soc. Ser. B 30 (1968), pp. 248–275.
   Google Scholar
• F. Cribari-Neto and T.C. Souza, Religious belief and intelligence: Worldwide evidence, Intelligence 41 (2013), pp. 482–489. doi: 10.1016/j.intell.2013.06.011
   Web of Science ®Google Scholar
• A.J. Dobson, An Introduction to Generalized Linear Models, 2nd ed., Chapman and Hall/CRC, London, 2001.
   Google Scholar
• S. Ferrari and F. Cribari-Neto, Beta regression for modelling rates and proportions, J. Appl. Stat. 31 (2004), pp. 799–815. doi: 10.1080/0266476042000214501
   Web of Science ®Google Scholar
• M.E. Ghitany, B. Atieh, and S. Nadarajah, Lindley distribution and its application, Math. Comput. Simul. 78 (2008), pp. 493–506. doi: 10.1016/j.matcom.2007.06.007
   Web of Science ®Google Scholar
• A.K. Gupta and S. Nadarajah, Handbook of Beta Distribution and its Applications, CRC Press, New York, 2004.
   Google Scholar
• M. Hunger, J. Baumert, and R. Holle, Analysis of sf-6d index data: Is beta regression appropriate? Value Health 14 (2011), pp. 759–767. doi: 10.1016/j.jval.2010.12.009
   PubMed Web of Science ®Google Scholar
• P. Jodrá, Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function, Math. Comput. Simul. 81 (2010), pp. 851–859. doi: 10.1016/j.matcom.2010.09.006
   Web of Science ®Google Scholar
• N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, 2nd ed., Vol. 2, John Wiley & Sons Inc., New York: 1995.
   Google Scholar
• R. Kieschnick and B.D. McCullough, Regression analysis of variates observed on (0, 1): Percentages, proportions and fractions, Stat. Model. 3 (2003), pp. 193–213. doi: 10.1191/1471082X03st053oa
   Web of Science ®Google Scholar
• S. Kotz and L.Y. M. Pensky, The Stress-Strength Model and its Generalizations: Theory and Applications, World Scientific, London, 2003.
   Google Scholar
• J.F. Lawless, Statistical Models and Methods for Lifetime Data, 2nd ed: John Wiley and Sons, Hoboken, NJ, 2003.
   Google Scholar
• E.J. Lehmann and G. Casella, Theory of Point Estimation, Springer Verlag, New York, 1998.
   Google Scholar
• D.V. Lindley, Fiducial distributions and Bayes' theorem, J. R. Stat. Soc. Ser. B (Methodol.) 20 (1958), pp. 102–107.
   Google Scholar
• J. Mazucheli, A.F.B. Menezes, and S. Chakraborty, On the one parameter unit-Lindley distribution and its associated regression model for proportion data (2018). Available at arXiv preprint arXiv:1801.02512
   Google Scholar
• J. Mazucheli, L.B. Fernandes, and R.P. Oliveira, LindleyR: The Lindley Distribution and Its Modifications, (2016). R package version 1.1.0.
   Google Scholar
• P. McCullagh and J. Nelder, Generalized Linear Models, 2nd ed. Chapman and Hall, London, 1989.
   Google Scholar
• L.E. Papke and J.M. Wooldridge, Econometric methods for fractional response variables with an application to 401(k) plan participation rates, J. Appl. Econometrics 11 (1996), pp. 619–632. doi: 10.1002/(SICI)1099-1255(199611)11:6<619::AID-JAE418>3.0.CO;2-1
   Web of Science ®Google Scholar
• SAS, The NLMIXED Procedure, SAS/STAT® User's Guide, Version 9.22, SAS Institute Inc., Cary, NC, 2010.
   Google Scholar
• T.C. Souza and F. Cribari-Neto, Intelligence, religiosity and homosexuality non-acceptance: Empirical evidence, Intelligence 52 (2015), pp. 63–70. doi: 10.1016/j.intell.2015.07.003
   Web of Science ®Google Scholar
• C.W. Topp and F.C. Leone, A family of J-Shaped frequency functions, J. Amer. Statist. Assoc. 50 (1955), pp. 209–219. doi: 10.1080/01621459.1955.10501259
   Web of Science ®Google Scholar
• D. Veberič, Lambert W function for applications in physics, Comput. Phys. Commun. 183 (2012), pp. 2622–2628. doi: 10.1016/j.cpc.2012.07.008
   Web of Science ®Google Scholar
• Q.H. Vuong, Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica 57 (1989), pp. 307–333. doi: 10.2307/1912557
   Web of Science ®Google Scholar
• S. Wang, Premium calculation by transforming the layer premium density, ASTIN Bull. 26 (1996), pp. 71–92. doi: 10.2143/AST.26.1.563234
   Google Scholar