Approximate Bayesian Estimation of the Parameters of Laplace Distribution

The Laplacian distribution is one of the most important distributions used to characterize the peak and thick-tailed data. This paper proposes a linear approximation Bayesian estimation with explicit solutions for the two parameters of the Laplace distribution. The superiority of linear approximate Bayesian estimation over other estimators is verified by theoretical derivation and numerical simulations, and the asymptotic behavior of the linear estimation with the increase of sample size is investigated.