The Laplace distribution is one of the oldest defined and studied distributions. In the one-parameter model (location parameter only), the sample median is the maximum likelihood estimator and is asymptotically efficient. Approximations for the variance of the sample median for small to moderate sample sizes have been studied, but no exact formula has been published. In this article, we provide an exact formula for the probability density function of the median and an exact formula for the variance of the median.
Cite this paper
J. Lawrence, "Distribution of the Median in Samples from the Laplace Distribution," Open Journal of Statistics
, Vol. 3 No. 6, 2013, pp. 422-426. doi: 10.4236/ojs.2013.36050
 P. S. Laplace, “Mémoire sur la Probabilité des Causes par les évènemens,” Mémoires de Mathematique et de Physique, Presentés à l’Académie Royale des Sciences, Par Divers Savans & Lus Dans ses Assemblées, Tome Sixième, 1774, pp. 621-656.
 N. L. Johnson, S. Kotz and N. Balakrishnan, “Continuous Univariate Distributions,” Vol. 1, Wiley, Hoboken, 1994.
 J. M. Keynes, “The Principal Averages and the Laws of Error Which Lead to Them,” Journal of the Royal Statistical Society, Vol. 74, No. 3, 1911, pp. 322-331.http://dx.doi.org/10.2307/2340444
 S. Kotz,, T. J. Kozubowski and K. Podgorski, “The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance (No. 183),” Springer, Berlin, 2001.http://dx.doi.org/10.1007/978-1-4612-0173-1
 J. T. Chu and & H. Hotelling, “The Moments of the Sample Median,” The Annals of Mathematical Statistics, Vol. 26, No. 4, 1955, pp. 593-606. http://dx.doi.org/10.1214/aoms/1177728419
 M. M. Siddiqui, “Approximations to the Moments of the Sample Median,” The Annals of Mathematical Statistics, Vol. 33, No. 1, 1962, pp. 157-168. http://dx.doi.org/10.1214/aoms/1177704720