A More Flexible Asymmetric Exponential Modification of the Laplace Distribution with Applications for Chemical Concentration and Environment Data

Jimmy Reyes, Mario A. Rojas, Pedro L. Cortés and Jaime Arrué ()
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Jimmy Reyes: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1270300, Chile
Mario A. Rojas: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1270300, Chile
Pedro L. Cortés: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1270300, Chile
Jaime Arrué: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1270300, Chile

Mathematics, 2022, vol. 10, issue 19, 1-19

Abstract: In this work, a new family of distributions based on the Laplace distribution is introduced. We define this new family by its stochastic representation as the sum of two independent random variables, one with a Laplace distribution and the other with an exponential distribution. Using a Monte Carlo simulation study, the statistical performance of the estimators obtained by the moments and maximum likelihood methods were empirically evaluated. We studied the coverage probabilities and mean length of the confidence intervals of the corresponding parameters based on the asymptotic normality of these estimators. This simulation study reported a good statistical performance of these estimators. Fits were made to three real data sets with the new distribution, two related to chemical concentrations and one to the environment, comparing it with three similar distributions given in the literature. We have used information criteria for the selection of models. These results showed that the exponentially modified Laplace model can be an alternative distribution to model skewed data with high kurtosis. The new approach is a contribution to the tools of statisticians and various professionals interested in modeling data with high kurtosis.

Keywords: exponentially modified Laplace distribution; moments; skewness and kurtosis coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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