Inference and Modeling with Log-concave Distributions

TL;DR

This paper reviews the theoretical properties and applications of log-concave distributions, highlighting their flexibility, computational tractability, and the absence of tuning parameters for inference.

Contribution

It provides a comprehensive review of recent advances in the theory and applications of log-concave distributions, emphasizing their practical advantages.

Findings

Log-concave distributions include most common parametric distributions.

MLE for log-concave distributions exists and is computationally accessible.

Log-concave models do not require tuning parameters like bandwidth.

Abstract

Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible nonparametric class of distributions. Further, the MLE exists and can be computed with readily available algorithms. Thus, no tuning parameter, such as a bandwidth, is necessary for estimation. Due to these attractive properties, there has been considerable recent research activity concerning the theory and applications of log-concave distributions. This article gives a review of these results.