Summary: We have introduced extensions \(\gamma_\nu (\alpha, x; b)\) and \(\Gamma_\nu (\alpha, x; b)\) of the generalized gamma functions \(\gamma (\alpha, x; b)\) and \(\Gamma (\alpha, x; b)\) considered recently in our paper J. Comput. Appl. Math. 55, No. 1, 99-124 (1994; Zbl 0833.33002). These extensions are found useful in the representations of the Laplace and \(K\)-transforms of a class of functions. We have also defined a generalization of the inverse Gaussian distribution. The cumulative and the reliability functions of the generalized inverse Gaussian distribution are expressed in terms of these functions. Some useful properties of the functions are also discussed.