AdequacyModel: An R package for probability distributions and general purpose optimization

Abstract

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see https://CRAN.R-project.org/package=Newdistns . It is also the basis of the Wrapped library (version 2.0), see https://CRAN.R-project.org/package=Wrapped . A third package making use of the AdequacyModel library can be found in https://CRAN.R-project.org/package=sglg . In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper.

The gamma Burr XII distributions: Theory and applications

“…The lower are these statistics, the better is the adjustment to the data. The MLEs and goodness-of-fit statistics are obtained using the AdequacyModel script in R software (Marinho et al, 2016). Table 3 provides a descriptive summary of the stress data.…”

The Zubair-dagum Distribution

“…The nonlinear equations above are then equated to zero and solved simultaneously to obtain the estimates of the parameters. The solutions cannot be solved analytically hence we solve numerically using the Adequacy package of Marinho et al [20] with "BFGS" algorithm. The R software [21] is used for this analysis.…”

Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

“…We used an Adequacy Model package by [33] in R by [34]. The goodness of fit analytical measures as highlighted in [33] was used in comparing the performances of the models. Smaller values of the measures indicate better model fit.…”