Stein's Method and the Laplace Distribution.
- Resource Type
- Article
- Authors
- Pike, John; Ren, Haining
- Source
- ALEA. Latin American Journal of Probability & Mathematical Statistics. 2014, Vol. 11, p571-587. 17p.
- Subject
- *LAPLACE distribution
*MATHEMATICAL statistics
*APPROXIMATION error
*RANDOM numbers
*RANDOM variables
- Language
- ISSN
- 1980-0436
Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary, we deduce a Berry-Esseen type theorem for the convergence of certain geometric sums. Our results make use of a second order characterizing equation and a distributional transformation which is related to zero-biasing. [ABSTRACT FROM AUTHOR]