Discover the relations and right-continuity properties of generalized inverses in distribution functions. Correcting misconceptions and introducing a new always right-continuous inverse.

The distribution function dose not, in general, have an inverse (in strict sense) as it may be not strictly increasing, for example, the PDF of a discrete random variable.

We examine the class of extended generalized inverse Gaussian (EGIG) distributions. This class of distributions, which appeared briefly in a monograph by J0rgensen (1982), is more deeply and broadly ...

The mathematical development of our mixture of generalized hyperbolic distributions model relies on its relationship with the generalized inverse Gaussian distribution. The latter is reviewed before ...

The buildup of a cortical neuron's excitation, called the postsynaptic potential (PSP), is well modeled by the generalized inverse Gaussian (First) Hitting Time (GIGHT) diffusion. Such a model is ...