Probability Distributions and Parameter Estimation

Implements an S4 distribution system and estimation methods for parameters of common distribution families. The common d, p, q, r function family for each distribution is enriched with the ll, e, and v counterparts, computing the log-likelihood, performing estimation, and calculating the asymptotic variance - covariance matrix, respectively. Parameter estimation is performed analytically whenever possible.

joker

Introduction

The joker R package develops an S4 distribution system and performs parameter estimation in common distribution families, making well-established and state-of-the-art methods more accessible.

Key Features

1. 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 estimator.

1. An S4-class distribution system is developed, allowing the generic evaluation of the dpqr function family and basic distribution calculus.
2. Moment functions (mean, median, mode, var, sd, skew, kurt) as well as functions that calculate the entropy and the Fisher Information are available for all distributions.
3. Distributions not included in base R are made available, such as the Dirichlet and the Multivariate Gamma.
4. Parameter estimation is performed analytically instead of numerically for the estimators that can be expressed explicitly.
5. 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. 7 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.

Installation

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

 install.packages("joker")

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

 devtools::install_github("thechibo/joker")

More details can be found in the joker Github repository.

Documentation

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

Team

The joker 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.