A Lindley-Type Distribution for Modeling High-Kurtosis Data

Abstract

This article proposes a heavy-tailed distribution for modeling positive data. The proposal arises with the ratio of independent random variables, specifically, a Lindley distribution divided by a beta distribution. This leads to a three-parameter extension of the Lindley distribution capable of modeling high levels of kurtosis. The main structural properties of the proposed distribution are derived. The skewness and kurtosis behavior of the distribution are described. Parameter estimation is discussed under consideration of the moment and maximum likelihood methods. Finally, in order to avoid the parameter non-identifiability problem, a two-parameter version of the proposed distribution is derived. The usefulness of this special case is illustrated by fitting data in two real scenarios.