@Article{RpackageFormula,
    title = {{Extended Model Formulas in \proglang{R}: Multiple Parts and
      Multiple Responses}},
    author = {Achim Zeileis and Yves Croissant},
    journal = {Journal of Statistical Software},
    year = {2010},
    volume = {34},
    number = {1},
    pages = {1--13},
    doi = {10.18637/jss.v034.i01},
  }

@Article{BB2009,
    title = {{\pkg{BB}: An \proglang{R} Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function}},
    author = {Ravi Varadhan and Paul Gilbert},
    journal = {Journal of Statistical Software},
    year = {2009},
    volume = {32},
    number = {4},
    pages = {1--26},
    url = {http://www.jstatsoft.org/v32/i04/},
  }

@article{stacy1962generalization,
  title={{A Generalization of the Gamma Distribution}},
  author={Stacy, Eo W},
  journal={The Annals of Mathematical Statistics},
  pages={1187--1192},
  year={1962},
  publisher={JSTOR}
}


@Manual{Rcore,
  title = {{\proglang{R}: A Language and Environment for Statistical Computing}},
  author = {{R Core Team}},
  organization = {R Foundation for Statistical Computing},
  address = {Vienna, Austria},
  year = {2017},
  url = {https://www.R-project.org/},
}

@article{tadikamalla1980look,
  title={{A Look at the Burr and Related Distributions}},
  author={Tadikamalla, Pandu R},
  journal={International Statistical Review/Revue Internationale de Statistique},
  pages={337--344},
  year={1980},
  publisher={JSTOR}
}


@book{mccullagh1989generalized,
 title={Generalized Linear Models, 2nd ed.,
        no. 37 in Monograph on Statistics and Applied Probability},
 author={McCullagh, Peter and Nelder, John A},
  year={1989},
  publisher={CRC press/Chapman \& Hall}
}

@Article{flexsurv2016,
    title = {\pkg{flexsurv}: A Platform for Parametric Survival Modeling in
      \proglang{R}},
    author = {Christopher Jackson},
    journal = {Journal of Statistical Software},
    year = {2016},
    volume = {70},
    number = {8},
    pages = {1--33},
    doi = {10.18637/jss.v070.i08},
  }


@Article{optimx2014,
    title = {Unifying Optimization Algorithms to Aid Software System
      Users: \pkg{optimx} for \proglang{R}},
    author = {John C. Nash and Ravi Varadhan},
    journal = {Journal of Statistical Software},
    year = {2011},
    volume = {43},
    number = {9},
    pages = {1--14},
    url = {http://www.jstatsoft.org/v43/i09/},
  }


@book{eddelbuettel2013seamless,
  title={Seamless \proglang{R} and \proglang{C++} Integration With Rcpp},
  author={Eddelbuettel, Dirk},
  year={2013},
  publisher={Springer-Verlag}
}

@Manual{RpackageCountr,
  title = {\pkg{Countr}: Flexible Univariate Count Models Based on Renewal Processes},
  author = {Tarak Kharrat and Georgi N. Boshnakov},
  year = {2016},
  note = {R package version 3.2.7},
  url = {https://cran.r-project.org/web/packages/Countr/index.html}
}


@article{winkelmann1995duration,
  title={Duration Dependence and Dispersion in Count-Data Models},
  author={Winkelmann, Rainer},
  journal={Journal of Business \& Economic Statistics},
  volume={13},
  number={4},
  pages={467--474},
  year={1995},
  publisher={Taylor \& Francis}
}

@article{baker2016Renewal,
  title={Event Count Distributions from Renewal Processes: Fast Computation of Probabilities},
  author={Baker, Rose and Kharrat, Tarak},
  journal={IMA Journal of Management Mathematics},
  year={2017},
  url = {http://dx.doi.org/10.1093/imaman/dpx008},
  publisher={Oxford University Press}
}

@book{press2007numerical,
  title={Numerical Recipes: The Art of Scientific Computing (3rd ed.)},
  author={Press, W H and Teukolsky, S A and Vetterling, W T and Flannery, B P},
  year={2007},
  publisher={Cambridge University Press}
}

@Manual{Rlang2015,
    title = {\proglang{R}: A Language and Environment for Statistical Computing},
    author = {{R Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2016},
    url = {https://www.R-project.org/},
  }

@article{McShane2008Count,
  title={Count Models Based on Weibull Inter-Arrival Times},
  author={McShane, Blake and Adrian, Moshe and Bradlow, Eric T and Fader, Peter S},
  journal={Journal of Business \& Economic Statistics},
  volume={26},
  number={3},
  year={2008}
}

@article{jose2011count,
  title={A Count Model Based on Mittag-Leffler Inter-Arrival Times},
  author={Jose, Kanichukattu K and Abraham, Bindu},
  journal={Statistica},
  volume={71},
  number={4},
  pages={501--514},
  year={2011},
  publisher={Department of Statistics, University of Bologna}
}

@article{Jose2013Gumbel,
  author = {Jose, K and Bindu Abraham},
  title = {A Counting Process with Gumbel Inter-Arrival Times for Modeling Climate Data},
  journal = {Journal of Environmental Statistics},
  volume = {4},
  number = {5},
  year ={2013},
  CODEN = {JESOBK},
  ISSN ={1945-1296},
  bibdate = {2012-09-17},
  URL = {http://jes.stat.ucla.edu/v04/i05},
  accepted = {2012-09-17},
  submitted = {2012-03-14},
}

@book{chambers1992statistical,
  title={Statistical Models in \proglang{S}},
  author={Chambers, J M and Hastie, T J},
  year={1992},
  publisher={Wadsworth \& Brooks/Cole, Pacific Grove, California},
}

@article{zeileis2008regression,
  title={Regression Models for Count Data in \proglang{R}},
  author={Zeileis, Achim and Kleiber, Christian and Jackman, Simon},
  journal={Journal of statistical software},
  volume={27},
  number={8},
  pages={1--25},
  year={2008},
  publisher={Foundation for Open Access Statistics}
}

@article{prentice1974log,
  title={A Log Gamma Model and Its Maximum Likelihood Estimation},
  author={Prentice, Ross L},
  journal={Biometrika},
  volume={61},
  number={3},
  pages={539--544},
  year={1974},
  publisher={Biometrika Trust}
}

@book{winkelmann2013econometric,
  title={Econometric Analysis of Count Data, 4th ed.},
  author={Winkelmann, Rainer},
  year={2013},
  publisher={Springer-Verlag, Berlin Heidelberg},
}

@book{cameron2013regression,
  title={Regression Analysis of Count Data, 2nd ed.},
  author={Cameron, A Colin and Trivedi, Pravin K},
  year={2013},
  publisher={Cambridge University Press}
}

@article{depril,
  title={Recursions for Convolutions of Arithmetic Distributions},
  author={De Pril, Nelson},
  journal={Astin Bulletin},
  volume={15},
  number={02},
  pages={135--139},
  year={1985},
  publisher={Cambridge Univ Press}
}

@book{feller1970,
  author = {Feller, William},
  title = {An Introduction to Probability Theory and Its Applications; 2nd ed.},
  publisher = {John Wiley \& Sons},
  address = "New York, NY",
  year = "1971",
}

@book{TarakPhd,
  title={A Journey Across Football Modelling with Application to Algorithmic Trading (PhD Thesis)},
  author={Kharrat, Tarak},
  year={2016},
  publisher={University of Manchester}
}


@article{bittner2007self,
  title={Self-Affirmation Model for Football Goal Distributions},
  author={Bittner, Elmar and Nussbaumer, Andreas and Janke, Wolfhard and Weigel, Martin},
  journal={EPL (Europhysics Letters)},
  volume={78},
  number={5},
  pages={58002},
  year={2007},
  publisher={IOP Publishing}
}

@Article{RcppArmadillo2014,
    title = {RcppArmadillo: Accelerating \proglang{R} With High-Performance \proglang{C++}
      Linear Algebra},
    author = {Dirk Eddelbuettel and Conrad Sanderson},
    journal = {Computational Statistics and Data Analysis},
    year = {2014},
    volume = {71},
    month = {March},
    pages = {1054--1063},
    url = {http://dx.doi.org/10.1016/j.csda.2013.02.005},
  }

@Manual{dplyr2016,
    title = {dplyr: A Grammar of Data Manipulation},
    author = {Hadley Wickham and Romain Francois},
    year = {2016},
    note = {R package version 0.5.0},
    url = {https://CRAN.R-project.org/package=dplyr},
  }

@Manual{xtable2016,
    title = {xtable: Export Tables to LaTeX or HTML},
    author = {David B. Dahl},
    year = {2016},
    note = {R package version 1.8-2},
    url = {https://CRAN.R-project.org/package=xtable},
}

@article{boshnakov2017bivariate,
  title={A Bivariate Weibull Count Model for Forecasting Association Football Scores},
  author={Boshnakov, Georgi and Kharrat, Tarak and McHale, Ian G},
  journal={International Journal of Forecasting},
  volume={33},
  number={2},
  pages={458--466},
  year={2017},
  publisher={Elsevier}
}

@article{dixon1998birth,
  title={A Birth Process Model for Association Football Matches},
  author={Dixon, Mark and Robinson, Michael},
  journal={Journal of the Royal Statistical Society D (The Statistician)},
  volume={47},
  number={3},
  pages={523--538},
  year={1998},
  publisher={Wiley Online Library}
}

@Manual{boot2017,
    title = {boot: Bootstrap R (S-PLUS) Functions},
    author = {Angelo Canty and B. D. Ripley},
    year = {2017},
    note = {R package version 1.3-20},
  }

@article{aitkin1978analysis,
  title={The Analysis of Unbalanced Cross-Classifications},
  author={Aitkin, Murray},
  journal={Journal of the Royal Statistical Society A (General)},
  pages={195--223},
  year={1978},
  publisher={JSTOR}
}

@Book{Venables20102MASS,
    title = {Modern Applied Statistics with S},
    author = {W. N. Venables and B. D. Ripley},
    publisher = {Springer-Verlag},
    edition = {Fourth},
    address = {New York},
    year = {2002},
    note = {ISBN 0-387-95457-0},
    url = {http://www.stats.ox.ac.uk/pub/MASS4},
  }

@Book{car2011,
    title = {An \proglang{R} Companion to Applied Regression},
    edition = {Second},
    author = {John Fox and Sanford Weisberg},
    year = {2011},
    publisher = {Sage},
    address = {Thousand Oaks {CA}},
    url = {http://socserv.socsci.mcmaster.ca/jfox/Books/Companion},
}

@book{davison1997bootstrap,
  title={Bootstrap Methods and Their Application},
  author={Davison, Anthony Christopher and Hinkley, David Victor},
  volume={1},
  year={1997},
  publisher={Cambridge University Press}
}

