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The estimators R package performs parameter estimation in common distribution families, making moment, maximum likelihood, and state-of-the-art estimators more accessible.

Key Features

  • The common d, p, q, r function family for each distribution (e.g. dnorm, pnorm, qnorm, rnorm) is enriched with
    • the ll counterpart (e.g. llnorm) that calculates the log-likelihood,
    • the e counterpart (e.g. enorm) that performs parameter estimation,
    • the v counterpart (e.g. vnorm) that calculates the asymptotic variance-covariance matrix of an estimators.
  • Distributions not included in base R are made available, such as the Dirichlet and the Multivariate Gamma.
  • Parameter estimation is performed analytically instead of numerically for the estimators that can be expressed explicitly.
  • Numerical optimization of the MLE (whenever required, e.g. the Beta and Gamma distributions) is performed with computational efficiency, taking advantage of the score equation system to reduce the dimensionality of the optimization.
  • Functions to compute and plot common estimator metrics (bias, variance, and RMSE) are included in the package to allow the convenient study and comparison of the estimators.
  • All functions can be used with the S4-Distribution system developed by the distr package family.


You can install the release version of estimators from CRAN by running the following line of code:


You can install the development version of estimators from github by running the following line of code:


More details can be found in the estimators Github repository.


Detailed documentation, along with reproducible examples, can be found in the package vignette vignette(topic = "estimators", package = "estimators").


The estimators package is developed in the Mathematics Department of the University of Athens. The package maintainer is Ioannis Oikonomidis, working under the supervision of Prof. Samis Trevezas.