Laplace record data

Basic properties of upper record values _XT(1),_XT(2),…,_XT(n)$X_{T(1)},X_{T(2)},\dots ,X_{T(n)}$ from a symmetric two-parameter Laplace distribution are established. In particular, unimodality of the density function and the exact expression of the mode are derived. Moreover, we obtain approximations of the first and second moment and the variance of _XT(k)$X_{T(k)}$ which provide close approximations even for moderate k. Additionally, limit laws and simulation of Laplace records are considered. Finally, we discuss maximum likelihood estimation in a location-scale family of Laplace distributions. We obtain nice representations of the estimators provided that the location parameter is unknown and present interesting properties of the established estimators. Some illustrative examples complete the presentation.