A comparative analysis on the performance of Lehman type II inverse Gaussian model and standard inverse Gaussian model in terms of flexibility

Searching for flexible parametric models is often the concern of statisticians in data analysis. In order to provide significantly skewed, flexible and heavy-tails models, more parameters are introduced into the existing models. In this paper, a novel univariate model called Lehmann type II inverse Gaussian model is constructed from standard inverse Gaussian distribution. The performance of the new distribution in terms of flexibility is compared with that of the baseline distribution. The construction of the new distribution is achieved by adding a shape parameter to the standard inverse Gaussian through dual transformation of the exponentiated generalized class of distributions. The idea is to verify if the Lehman type II inverse Gaussian model would perform better than the inverse Gaussian distribution in modeling real life situations. Various basic statistical properties of the proposed distribution, including the likelihood function are derived. Parameter estimates are obtained via maximum likelihood estimation method. The ratio of maximized likelihoods and Akaike Information Criteria (AIC) are employed to select the best model. In conclusion, when the two models are applied to two known real lifetime data sets, Lehmann inverse Gaussian shows more flexibility in modeling skew data than inverse Gaussian distribution as evident in the negative sign of likelihoods ratio and lower value of AIC