A Supplement to the Gaussian Transform of Distributions

A paper by Alecu et al. introduced the novel concept of Gaussian transform distributions. In this correspondence, we derive a comprehensive collection of formulas for the inverse Gaussian transforms distribution. Also derived are the statistical procedures (determined by the method of moments) for estimating the parameters of the transforms. It is expected that this correspondence could serve as an important reference and could be useful for the application areas discussed by Alecu et al.