We derive maximum likelihood estimators for the parameters of the Laplace distribution for interval censored data. Existence and uniqueness of the estimators are proved. Simulations and real data applications show that the Laplace distribution can be a better model for interval censored data than competing models in spite of being simpler.
"Estimation of parameters in Laplace distributions with interval censored data." Braz. J. Probab. Stat. 29 (3) 677 - 694, August 2015. https://doi.org/10.1214/14-BJPS239