A Bayesian-Weighted Inverse Gaussian Regression Model with Application to Seismological Data

Table 2

A general comparison of strengths and limitations of different discussed models.

Regression model	Strengths	Limitations
LN (see, for example, [32])	(i) The LN regression model is the most famous traditional candidate for analyzing positive right-skewed response observations; (ii) It can be fitted and interpreted easily based on a normal model by using a simple log transformation	(i) Moments of the response variable depend overly on exact log-normality assumption; (ii) Small sample sequential moments of the response variable oscillate to excess as the sample size increases; (iii) The distribution of response variable has too thick right-hand tail to be plausible; (iv) LN distribution is also almost symmetrical, and there is no way to control the skewness or asymmetry of the distribution
IG (see, for example, [18, 22, 23, 35])	(i) The sampling theory of the response observations is tractable; (ii) There has been a growing attention to the use of IG distribution, and recent researches have revealed rigid evidence supporting the IG distribution in comparison with the log-normal in most applications	Fitting procedure under IG distribution is more complicated than corresponding procedure for LN model
WIG (see, for example, [18, 22, 23, 35])	(i) The sampling theory of the response observations is tractable; (ii) There has been a growing attention to the use of IG distribution, and recent researches have revealed rigid evidence supporting the IG distribution in comparison with the log-normal in most applications	Fitting procedure for WIG model is more complicated than corresponding procedure in IG model