@article{Dorsey1995,
author = {Dorsey, Robert E. and Mayer, Walter J.},
doi = {10.2307/1392521},
issn = {07350015},
journal = {Journal of Business {\&} Economic Statistics},
month = {jan},
number = {1},
pages = {53},
title = {{Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability, and Other Irregular Features}},
url = {https://www.jstor.org/stable/1392521?origin=crossref},
volume = {13},
year = {1995}
}
@article{Gurland1954,
author = {Gurland, John},
doi = {10.1080/03461238.1954.10414197},
issn = {0346-1238},
journal = {Scandinavian Actuarial Journal},
month = {jan},
number = {1},
pages = {71--76},
title = {{On regularity conditions for maximum likelihood estimators}},
url = {http://www.tandfonline.com/doi/abs/10.1080/03461238.1954.10414197},
volume = {1954},
year = {1954}
}
@inproceedings{Daniels1961,
address = {Berkeley},
author = {Daniels, H. E.},
booktitle = {Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics},
editor = {Neyman, Jerzy},
file = {:F$\backslash$:/Desktop/euclid.bsmsp.1200512164.pdf:pdf},
pages = {151--163},
publisher = {University of California Press},
title = {{Efficiency of a maximum likelihood estimator}},
year = {1961}
}
@incollection{Kruschke2015,
address = {Oxford, UK},
author = {Kruschke, J. K. and Vanpaemel, W.},
booktitle = {Bayesian estimation in hierarchical models},
chapter = {13},
pages = {279--281},
publisher = {Oxford University Press},
title = {{The Oxford Handbook of Computational and Mathematical Psychology}},
year = {2015}
}
@book{Davison1997,
address = {Cambridge},
annote = {ISBN 0-521-57391-2},
author = {Davison, A C and Hinkley, D V},
publisher = {Cambridge University Press},
title = {{Bootstrap Methods and Their Applications}},
url = {http://statwww.epfl.ch/davison/BMA/},
year = {1997}
}
@manual{Canty2017,
annote = {R package version 1.3-20},
author = {Canty, Angelo and Ripley, B D},
title = {{boot: Bootstrap R (S-Plus) Functions}},
year = {2017}
}
@book{Pawitan2013,
author = {Pawitan, Yudi},
isbn = {978-0199671229},
publisher = {Oxford University Press},
title = {{In all likelihood: statistical modelling and inference using likelihood}},
year = {2013}
}
@article{MurdockBennetB.1961,
author = {{Murdock, Bennet B.}, Jr.},
doi = {10.1037/h0043657},
issn = {0022-1015},
journal = {Journal of Experimental Psychology},
number = {6},
pages = {618--625},
title = {{The retention of individual items.}},
url = {http://content.apa.org/journals/xge/62/6/618},
volume = {62},
year = {1961}
}
@article{Myung2003,
author = {Myung, In Jae},
doi = {10.1016/S0022-2496(02)00028-7},
issn = {00222496},
journal = {Journal of Mathematical Psychology},
month = {feb},
number = {1},
pages = {90--100},
title = {{Tutorial on maximum likelihood estimation}},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0022249602000287},
volume = {47},
year = {2003}
}
@article{Devendra2013,
author = {Devendra, K. and Rangaswamy, T.},
doi = {10.4236/jmmce.2013.16054},
issn = {2327-4077},
journal = {Journal of Minerals and Materials Characterization and Engineering},
number = {06},
pages = {353--357},
title = {{Strength Characterization of E-glass Fiber Reinforced Epoxy Composites with Filler Materials}},
url = {http://www.scirp.org/journal/doi.aspx?DOI=10.4236/jmmce.2013.16054},
volume = {01},
year = {2013}
}
@book{Fletcher1987,
address = {New York},
author = {Fletcher, Roger},
edition = {2nd},
isbn = {978-0-471-91547-8},
publisher = {John Wiley {\&} Sons},
title = {{Practical Methods of Optimization}},
year = {1987}
}
@article{Dennis1981,
author = {Dennis, John E. and Gay, David M. and Walsh, Roy E.},
doi = {10.1145/355958.355965},
issn = {00983500},
journal = {ACM Transactions on Mathematical Software},
month = {sep},
number = {3},
pages = {348--368},
title = {{An Adaptive Nonlinear Least-Squares Algorithm}},
url = {https://dl.acm.org/doi/10.1145/355958.355965},
volume = {7},
year = {1981}
}
@techreport{Singer2009,
author = {Singer, Sa{\v{s}}a and Nelder, John},
booktitle = {Scholarpedia},
doi = {10.4249/scholarpedia.2928},
issn = {1941-6016},
number = {7},
pages = {2928},
title = {{Nelder-Mead algorithm}},
url = {http://www.scholarpedia.org/article/Nelder-Mead{\_}algorithm},
volume = {4},
year = {2009}
}
@incollection{Mathews2004,
abstract = {A simplex method for finding a local minimum of a function of several variables has been devised by Nelder and Mead. For two variables, a simplex is a triangle, and the method is a pattern search that compares function values at the three vertices of a triangle. The worst vertex, where f (x, y) is largest, is rejected and replaced with a new vertex. A new triangle is formed and the search is continued. The process generates a sequence of triangles (which might have different shapes), for which the function values at the vertices get smaller and smaller. The size of the triangles is reduced and the coordinates of the minimum point are found. The algorithm is stated using the term simplex (a generalized triangle in N di-mensions) and will find the minimum of a function of N variables. It is effective and computationally compact. SEC. 8.2 NELDER-MEAD AND POWELL'S METHODS 431 Initial Triangle BGW Let f (x, y) be the function that is to be minimized. To start, we are given three vertices of a triangle: V k = (x k , y k), k = 1, 2, 3. The function f (x, y) is then evaluated at each of the three points: z k = f (x k , y k) for k = 1, 2, 3. The subscripts are then reordered so that z 1 ≤ z 2 ≤ z 3 . We use the notation (5) B = (x 1 , y 1), G = (x 2 , y 2), and W = (x 3 , y 3)},
author = {Mathews, J. H. and Fink, K. K.},
booktitle = {Numerical Methods Using Matlab},
edition = {4th},
isbn = {9780387987934},
pages = {430--437},
publisher = {TBS},
title = {{Nelder-Mead method}},
year = {2004}
}
@article{Byrd1995,
author = {Byrd, Richard H. and Lu, Peihuang and Nocedal, Jorge and Zhu, Ciyou},
doi = {10.1137/0916069},
issn = {1064-8275},
journal = {SIAM Journal on Scientific Computing},
month = {sep},
number = {5},
pages = {1190--1208},
title = {{A Limited Memory Algorithm for Bound Constrained Optimization}},
url = {http://epubs.siam.org/doi/10.1137/0916069},
volume = {16},
year = {1995}
}
@manual{R2019,
address = {Vienna, Austria},
author = {{R Core Team}},
organization = {R Foundation for Statistical Computing},
title = {{R: A Language and Environment for Statistical Computing}},
url = {https://www.r-project.org/},
year = {2019}
}
@book{Chambers+Hastie:1992,
address = {London},
editor = {Chambers, John M and Hastie, Trevor J},
publisher = {Chapman {\&} Hall},
title = {{Statistical Models in $\backslash$proglang{\{}S{\}}}},
year = {1992}
}
@article{Zeileis+Kleiber+Jackman:2008,
author = {Zeileis, Achim and Kleiber, Christian and Jackman, Simon},
doi = {10.18637/jss.v027.i08},
journal = {Journal of Statistical Software},
number = {8},
pages = {1--25},
title = {{Regression Models for Count Data in $\backslash$proglang{\{}R{\}}}},
volume = {27},
year = {2008}
}
@book{Nash1979,
address = {Bristol},
author = {Nash, John C.},
edition = {2nd Editio},
publisher = {Adam Hilger},
title = {{Compact Numerical Methods for Computers. Linear Algebra and Function Minimisation}},
year = {1979}
}
@article{Nelder1965,
author = {Nelder, J. A. and Mead, R.},
doi = {10.1093/comjnl/7.4.308},
issn = {0010-4620},
journal = {The Computer Journal},
month = {jan},
number = {4},
pages = {308--313},
title = {{A Simplex Method for Function Minimization}},
url = {https://academic.oup.com/comjnl/article-lookup/doi/10.1093/comjnl/7.4.308},
volume = {7},
year = {1965}
}
@article{Gay1990,
author = {Gay, David M},
journal = {AT{\&}T Bell Laboratories, Murray Hill, NJ 07974},
number = {153},
pages = {1--21},
title = {{Usage summary for selected optimization routines - Computing Science technical report number 153}},
year = {1990}
}
@article{Fox1978,
author = {Fox, P. A. and Hall, A. P. and Schryer, N. L.},
doi = {10.1145/355780.355783},
issn = {00983500},
journal = {ACM Transactions on Mathematical Software},
month = {jun},
number = {2},
pages = {104--126},
title = {{The PORT Mathematical Subroutine Library}},
url = {https://dl.acm.org/doi/10.1145/355780.355783},
volume = {4},
year = {1978}
}
@article{Yee:2009,
author = {Yee, Thomas W},
doi = {10.18637/jss.v032.i10},
journal = {Journal of Statistical Software},
number = {10},
pages = {1--34},
title = {{The $\backslash$pkg{\{}VGAM{\}} Package for Categorical Data Analysis}},
volume = {32},
year = {2010}
}
@book{McCullagh+Nelder:1989,
address = {London},
author = {McCullagh, Peter and Nelder, John A},
doi = {10.1007/978-1-4899-3242-6},
edition = {2nd},
publisher = {Chapman {\&} Hall},
title = {{Generalized Linear Models}},
year = {1989}
}
@article{Stasinopoulos+Rigby:2007,
author = {Stasinopoulos, D Mikis and Rigby, Robert A},
doi = {10.18637/jss.v023.i07},
journal = {Journal of Statistical Software},
number = {7},
pages = {1--46},
title = {{Generalized Additive Models for Location Scale and Shape ({\{}GAMLSS{\}}) in $\backslash$proglang{\{}R{\}}}},
volume = {23},
year = {2007}
}
@article{Mullahy:1986,
author = {Mullahy, John},
doi = {10.1016/0304-4076(86)90002-3},
journal = {Journal of Econometrics},
number = {3},
pages = {341--365},
title = {{Specification and Testing of Some Modified Count Data Models}},
volume = {33},
year = {1986}
}
@book{Cameron+Trivedi:2013,
address = {Cambridge},
author = {Cameron, A Colin and Trivedi, Pravin K},
edition = {2nd},
publisher = {Cambridge University Press},
title = {{Regression Analysis of Count Data}},
year = {2013}
}
@book{Wood:2006,
address = {Boca Raton},
author = {Wood, Simon N},
publisher = {Chapman {\&} Hall/CRC},
title = {{Generalized Additive Models: An Introduction with $\backslash$proglang{\{}R{\}}}},
year = {2006}
}
@manual{Jackman:2015,
annote = {$\backslash$proglang{\{}R{\}} package version 1.4.9},
author = {Jackman, Simon},
title = {{$\backslash$pkg{\{}pscl{\}}: Classes and Methods for $\backslash$proglang{\{}R{\}} Developed in the Political Science Computational Laboratory, Stanford University}},
url = {https://cran.r-project.org/package=pscl},
year = {2015}
}
@manual{R,
address = {Vienna, Austria},
author = {{$\backslash$proglangR Core Team}},
organization = {$\backslash$proglang{\{}R{\}} Foundation for Statistical Computing},
title = {{$\backslash$proglang{\{}R{\}}: {\{}A{\}} Language and Environment for Statistical Computing}},
url = {https://www.r-project.org/},
year = {2017}
}
@book{Venables+Ripley:2002,
address = {New York},
author = {Venables, William N and Ripley, Brian D},
doi = {10.1007/978-0-387-21706-2},
edition = {4th},
pages = {495},
publisher = {Springer-Verlag},
title = {{Modern Applied Statistics with $\backslash$proglang{\{}S{\}}}},
year = {2002}
}
@article{Fisher1922,
author = {Fisher, R. A.},
doi = {10.1098/rsta.1922.0009},
issn = {1364-503X},
journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
month = {jan},
number = {594-604},
pages = {309--368},
title = {{On the Mathematical Foundations of Theoretical Statistics}},
url = {http://rsta.royalsocietypublishing.org/cgi/doi/10.1098/rsta.1922.0009},
volume = {222},
year = {1922}
}
@article{Fisher1912,
author = {Fisher, Ronald},
doi = {10.2307/2246266},
issn = {08834237},
journal = {Messenger of Mathematics},
number = {1},
pages = {155--160},
title = {{On an Absolute Criterion for Fitting Frequency Curves}},
volume = {41},
year = {1912}
}
@article{Stasinopoulos2007,
abstract = {GAMLSS is a general framework for fitting regression type models where the distribution of the response variable does not have to belong to the exponential family and includes highly skew and kurtotic continuous and discrete distribution. GAMLSS allows all the parameters of the distribution of the response variable to be modelled as linear/non-linear or smooth functions of the explanatory variables. This paper starts by defining the statistical framework of GAMLSS, then describes the current implementation of GAMLSS in R and finally gives four different data examples to demonstrate how GAMLSS can be used for statistical modelling.},
author = {Stasinopoulos, D. Mikis and Rigby, Robert A.},
doi = {10.18637/jss.v023.i07},
issn = {1548-7660},
journal = {Journal of Statistical Software},
number = {7},
title = {{Generalized Additive Models for Location Scale and Shape (GAMLSS) in R}},
url = {http://www.jstatsoft.org/v23/i07/},
volume = {23},
year = {2007}
}
@incollection{Stasinopoulos2017,
abstract = {This book series reflects the recent rapid growth in the development and application of R, the programming language and software environment for statistical computing and graphics. R is now widely used in academic research, education, and industry. It is constantly growing, with new versions of the core software released regularly and more than 10,000 packages available. It is difficult for the documentation to keep pace with the expansion of the software, and this vital book series provides a forum for the publication of books covering many aspects of the development and application of R. The scope of the series is wide, covering three main threads: • Applications of R to specific disciplines such as biology, epidemiology, genetics, engineering, finance, and the social sciences. • Using R for the study of topics of statistical methodology, such as linear and mixed modeling, time series, Bayesian methods, and missing data. • The development of R, including programming, building packages, and graphics. The books will appeal to programmers and developers of R software, as well as applied statisticians and data analysts in many fields. The books will feature detailed worked examples and R code fully integrated into the text, ensuring their usefulness to researchers, practitioners and students.},
author = {Stasinopoulos, Mikis and Rigby, Robert A. and Heller, Gillian Z. and Voudouris, Vlasios and {De Bastiani}, Fernanda},
booktitle = {Flexible regression and smoothing using GAMLSS in R},
isbn = {9781138197909},
pages = {153--189},
publisher = {CRC Press},
title = {{The GAMLSS family of distributions}},
year = {2017}
}
@article{Ghitany2013,
abstract = {A new two-parameter power Lindley distribution is introduced and its properties are discussed. These include the shapes of the density and hazard rate functions, the moments, skewness and kurtosis measures, the quantile function, and the limiting distributions of order statistics. Maximum likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Three algorithms are proposed for generating random data from the proposed distribution. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators of the parameters as well as the coverage probability and the width of the confidence interval for each parameter. An application of the model to a real data set is presented finally and compared with the fit attained by some other well-known two-parameter distributions. {\textcopyright} 2013 Elsevier B.V. All rights reserved.},
author = {Ghitany, M. E. and Al-Mutairi, D. K. and Balakrishnan, N. and Al-Enezi, L. J.},
doi = {10.1016/j.csda.2013.02.026},
file = {:C$\backslash$:/Users/USUARIO/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ghitany et al. - 2013 - Power Lindley distribution and associated inference.pdf:pdf},
issn = {01679473},
journal = {Computational Statistics and Data Analysis},
keywords = {Lambert function,Maximum likelihood estimator,Power Lindley distribution,Simulation algorithms},
pages = {20--33},
publisher = {Elsevier B.V.},
title = {{Power Lindley distribution and associated inference}},
url = {http://dx.doi.org/10.1016/j.csda.2013.02.026},
volume = {64},
year = {2013}
}
@article{Bakouch2012,
abstract = {A new continuous distribution is introduced by compounding exponentiated exponential and binomial distributions, named as exponentiated exponential binomial (EEB) distribution. This distribution has the ability to model lifetime data with increasing, decreasing and upside-down bathtub shaped failure rates. Moreover, the zero-truncated binomial distribution used in compounding is overdispersed. Some properties of the distribution are investigated. Estimation and inference procedure for the distribution parameters are discussed. An application to real data demonstrates that the EEB distribution can provide a better fit than a recent class of lifetime distributions. {\textcopyright} 2012 Elsevier B.V.},
author = {Bakouch, Hassan S. and Risti{\'{c}}, Miroslav M. and Asgharzadeh, A. and Esmaily, L. and Al-Zahrani, Bander M.},
doi = {10.1016/j.spl.2012.03.004},
file = {:C$\backslash$:/Users/USUARIO/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Bakouch et al. - 2012 - An exponentiated exponential binomial distribution with application.pdf:pdf},
issn = {01677152},
journal = {Statistics and Probability Letters},
keywords = {62E99,Binomial distribution,Exponentiated exponential distribution,Hazard rate,Residual life,Stress-strength parameter},
number = {6},
pages = {1067--1081},
publisher = {Elsevier B.V.},
title = {{An exponentiated exponential binomial distribution with application}},
url = {http://dx.doi.org/10.1016/j.spl.2012.03.004},
volume = {82},
year = {2012}
}
@article{Whitmore1983,
author = {Whitmore, G. A.},
doi = {10.2307/3314888},
issn = {03195724},
journal = {Canadian Journal of Statistics},
month = {dec},
number = {4},
pages = {305--315},
title = {{A regression method for censored inverse-Gaussian data}},
url = {http://doi.wiley.com/10.2307/3314888},
volume = {11},
year = {1983}
}
