A class of continuous kernels and Cauchy type heavy tail distributions

We shed light on an interesting class of one sided continuous kernels on [0, infinity). Then we present its properties, provide new integral formulas including an extension for the Kotz and Ostrovskii (1996) mixture representation, introduce a class of Cauchy type distributions, and finally enlarge the class of one sided stable densities. This study provides powerful tools in modeling erratic continuous data.