Alternate asymmetric Laplace distribution: Properties and applications

Abstract

In this article, we introduce a one parameter asymmetric version of the standard Laplace distribution, named “the alternate asymmetric Laplace distribution (AALD)”. The proposed model extends the classical Laplace law through the inclusion of a single shape parameter ρ. While most of the existing asymmetric models rely on multiple shape parameters and lack closed-form expressions for higher-order characteristics, the AALD, with its single parameter structure, offers analytical tractability and flexibility. Specifically, closed-form expressions are derived for the cumulative distribution function, moment generating function, quantiles, entropy, and order statistics, underscoring the theoretical richness of the model. The location-scale extension of AALD, named “the extended alternate asymmetric Laplace distribution (EAALD)” is introduced and studied in detail. The estimation and testing procedures for the parameters of EAALD are discussed and the performance of the obtained estimators is examined through a simulation study. Through applications to two real-world data sets from distinct domains, EAALD consistently provides a superior fit compared to the established asymmetric models, highlighting both its methodological novelty and practical relevance.

Journal of Statistical Research 2026, Vol. 60, No. 1, pp. 1-31.