Semiparametric Gaussian Variance-Mean Mixtures for Heavy-Tailed and Skewed Data

Table 2

Quantile estimates are obtained from models fitted to the observed dataset using maximum likelihood estimation. To obtain the maximum likelihood estimators in skewed-Gaussian and 𝑡-distributions, the sn R package is used [27].

Quantiles	Observed	Gaussian	Skewed Gaussian	Skewed 𝑡
2.5%	−1.474	−1.960	−1.451	−1.446
5%	−1.328	−1.645	−1.306	−1.300
25%	−0.738	−0.674	−0.751	−0.749
50%	−0.175	0.000	−0.173	−0.185
75%	0.555	0.674	0.590	0.566
95%	1.783	1.645	1.887	1.895
97.5%	2.394	1.960	2.339	2.379