Approximation of the quasi‐deviance function for the time‐changed Lévy processes by the first‐exit time of the inverse Gaussian subordinator

In this paper, we approximate the link and variance functions of the natural exponential family generated by the distribution of the class of time‐changed Lévy processes by the first‐exit time of the inverse Gaussian subordinator. These results lead us to get an approximation for the quasi‐deviance function.