A New Modification in the Classical Laplace Distribution

Several modifications of the Laplace distribution have been introduced and applied in various fields up to this dayý. ýIn this paperý, ýwe introduce a modified symmetric version of the classical Laplace distributioný. ýWe provide a comprehensive theoretical description of this distributioný. ýIn particularý, ýwe derive the formulas for the $k$th momentý, ýquantiles and several useful alternative representations of the distributioný. ýWe derive the maximum likelihood estimators of the parameters and investigate their properties via simulationý. ýFinallyý, ýwe analyse three real-world datasets to illustrate the usefulness of the modified classical Laplace distributioný. ýThe results suggest that further improvement to classical Laplace distribution fitting is possible and the new model provides an attractive alternative to the classical Laplace distribution.