A folded Laplace distribution

We study a class of probability distributions on the positive real line, which arise by folding the classical Laplace distribution around the origin. This is a two-parameter, flexible family with a sharp peak at the mode, very much in the spirit of the classical Laplace distribution. We derive basic properties of the distribution, which include the probability density function, distribution function, quantile function, hazard rate, moments, and several related parameters. Further properties related to mixture representation, Lorenz curve, mean residual life, and entropy are included as well. We also discuss parameter estimation for this new stochastic model and illustrate its potential applications with real data.

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