Abstract
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.
Highlights
1 Introduction We present a theory of a class of distributions on R+ = [ 0, ∞), obtained by folding the classical Laplace distribution given by the probability density function (PDF)
A random variable on R+ given by the density function (4), where μ ≥ 0 and σ > 0, is said to have a folded Laplace distribution, denoted by FL(μ, σ )
By taking the derivatives of the moment generating function (MGF) at t = 0, we can recover the moments of the FL distribution
Summary
A random variable on R+ given by the density function (4), where μ ≥ 0 and σ > 0, is said to have a folded Laplace distribution, denoted by FL(μ, σ ). By taking the derivatives of the MGF at t = 0, we can recover the moments of the FL distribution The latter are given in the following result, whose lengthy albeit routine derivation shall be omitted [details can be found in Liu (2014)]. A folded Laplace variable truncated below at μ, W = Y |Y ≥ μ, has an exponential distribution with mean σ , shifted by μ units to the right, so its PDF is h2(y) =.
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