Two-Sided Lindley Distribution with Inference and Applications

Abstract

We propose a new distribution, called two-sided Lindley distribution. Some of its statistical properties are derived including the probability and cumulative density functions, moments and quantile function. The proposed distribution is applied to GARCH volatility model. An application on Nikke-225 index is given to demonstrate the performance of GARCH model specified under two-sided Lindley innovation distribution against to normal, Student's-t, skew-normal and skew-T models based on the forecasting accuracy of value-at-risk. It is concluded that GARCH model with two-sided Lindley innovation distribution provides better fits than other competitive models and produce the most accurate value-at-risk forecasts among others.