The skew-symmetric-Laplace-uniform distribution

TL;DR

This paper introduces the skew-symmetric-Laplace-uniform distribution (SSLUD), a new family of skewed distributions that models asymmetry and bounded support, with properties, estimation methods, and real data application.

Contribution

It proposes a novel skew distribution combining Laplace and uniform distributions, with detailed properties, estimation techniques, and practical application to financial data.

Findings

Maximum likelihood estimator outperforms moment estimator in simulations.

SSLUD effectively models asymmetric, bounded financial data.

The distribution fits real stock market data well.

Abstract

Laplace distribution is popular in the field of economics and finance. Still, data sets often show a lack of symmetry and a tendency of being bounded from either side of their support. In view of this, we introduce a new family of skew distribution using the skewing mechanism of Azzalini (1985), namely, skew-symmetric-Laplace-uniform distribution (SSLUD). Here uniform distribution is used not only to introduce skewness in Laplace distribution but also to restrict distribution support on one side of the real line. This paper provides a comprehensive description of the essential distributional properties of SSLUD. Estimators of the parameter are obtained using the method of moments and the method of maximum likelihood. The finite sample and asymptotic properties of these estimators are studied using simulation. It is observed that the maximum likelihood estimator is better than the moment estimator through a simulation study. Finally, an application of SSLUD to real-life data on the daily percentage change in the price of NIFTY 50, an Indian stock market index, is presented.