Modified Laplace Distribution, Its Statistical Properties and Applications

Abstract

Increasing the parameter of a distribution helps to capture the skewness and peakedness characteristic in the data sets. This allows a more realistic modeling of data arising from different real life situations. In this paper, we modified Laplace distribution using the exponentiation method. The study proved that the modified Laplace distribution (MLD) is a probability density function. Some of the basic statistical properties of the modified Laplace distribution are obtained. We applied the proposed modified Laplace distribution on two life datasets and simulated data. Parameters of the distributions were estimated using method of maximum likelihood estimation. The study compared the modified Laplace distribution with Laplace distribution and Generalized error distribution using Schwartz Criteria (SC) measure of fitness. The results obtained revealed that the modified Laplace distribution has a better fit than the Laplace and Generalized error distributions and can be used for more realistic modeling of data arising from different real life situations. The simulation results obtained shows that as the sample size increases, the Biasedness and Root Mean Square Error (RMSE) of the proposed modified Laplace distribution reduces.