Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach

Abstract

We develop a likelihood-ratio test for discriminating between the g-and-h and the g distribution, which is a special case of the former obtained when the parameter h is equal to zero. The g distribution is a shifted lognormal, and is therefore suitable for modeling economic and financial quantities. The g-and-h is a more flexible distribution, capable of fitting highly skewed and/or leptokurtic data, but is computationally much more demanding. Accordingly, in practical applications the test is a valuable tool for resolving the tractability-flexibility trade-off between the two distributions. Since the classical result for the asymptotic distribution of the test is not valid in this setup, we derive the null distribution via simulation. Further Monte Carlo experiments allow us to estimate the power function and to perform a comparison with a similar test proposed by Xu and Genton (Comput Stat Data Anal 91:78–91, 2015). Finally, the practical relevance of the test is illustrated by two risk management applications dealing with operational and actuarial losses.