Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Using real-coded genetic algorithms for Weibull parameter estimation
ICC&IE '94 Proceedings of the 17th international conference on Computers and industrial engineering
An approximate method for generating asymmetric random variables
Communications of the ACM
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Weighted quantile-based estimation for a class of transformation distributions
Computational Statistics & Data Analysis
Bayesian estimation of quantile distributions
Statistics and Computing
Robust measures of tail weight
Computational Statistics & Data Analysis
Likelihood-free Bayesian estimation of multivariate quantile distributions
Computational Statistics & Data Analysis
Simultaneous adjustment of bias and coverage probabilities for confidence intervals
Computational Statistics & Data Analysis
Robust estimation of the parameters of g-and-h distributions, with applications to outlier detection
Computational Statistics & Data Analysis
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Continuing increases in computing power and availability mean that many maximum likelihood estimation (MLE) problems previously thought intractable or too computationally difficult can now be tackled numerically. However, ML parameter estimation for distributions whose only analytical expression is as quantile functions has received little attention. Numerical MLE procedures for parameters of new families of distributions, the g-and-k and the generalized g-and-h distributions, are presented and investigated here. Simulation studies are included, and the appropriateness of using asymptotic methods examined. Because of the generality of these distributions, the investigations are not only into numerical MLE for these distributions, but are also an initial investigation into the performance and problems for numerical MLE applied to quantile-defined distributions in general. Datasets are also fitted using the procedures here. Results indicate that sample sizes significantly larger than 100 should be used to obtain reliable estimates through maximum likelihood.