Distributions
In univariateML: Maximum Likelihood Estimation for Univariate Densities

knitr::opts_chunk$set(echo = TRUE)

The implemented distributions are found in univariateML_models.

library("univariateML")
univariateML_models

This package follows a naming convention for the ml*** functions. To access the documentation of the distribution associated with an ml*** function, write package::d***. For instance, to find the documentation for the log-gamma distribution write

?actuar::dlgamma

Additional information about the models can found in univariateML_metadata.

univariateML_metadata[["mllgser"]]

From the metadata you can read that

mllgser estimates the parameters N and s.
Its a discrete distribution on $1,2,3,...$,
Its density function is extraDistr::dlgser.

Problematic Distributions

Some estimation procedures will fail under certain circumstances. Sometimes due to numerical problems, but also because the maximum likelihood estimator fails to exist. Here is a possibly non-exhaustive list of known problematic distributions.

Discrete distributions

Binomial. The maximum likelihood estimator does not exist for underdispersed data (when $size$ is estimated). There is an increasing sequence of estimates $size$, $p$ so that the binomial likelihood converges to a Poisson, however.
Negative binomial. The same sort of problem occurs with the negative binomial, which converges to a Poisson for some data sets.
Lomax. Here we have convergence to an exponential for certain data sets.
Zipf. The optimal shape parameter may be negative, which still defines a density, but is not supported by extraDistr.
Logarithic series distribution. When all observations are $1$ the estimator does not exist, as the "actual" maximum likelihood estimator is the point mass on $0$.

Continuous distributions

Gompertz. Here we have a similar problem, with some parameters outside the range of the distribution converging to a density function with a different support. When the b parameter tends towards 0, the Gompertz tends towards an exponential. A failing estimation indicates the exponential has a better fit.
Lomax. Here we have convergence to an exponential for certain data sets.
Burr. The Burr distribution tends to the Pareto distribution when shape1*shape2 converges to a constant while shape2 tends to infinity.