Physical Sciences and Mathematics Commons^™

Advances In The Modeling Of Heavy-Tailed Distributions, Sang Jin Kang

Electronic Thesis and Dissertation Repository

Several advances are proposed in connection with the approximation and estimation of heavy-tailed distributions, some of which also apply to other types of distributions. It is first explained that on initially applying the Esscher transform to heavy-tailed density functions such as the Pareto, Student-t and Cauchy densities, one can utilize a moment-based technique whereby the tilted density functions are expressed as the product of a base density function and a polynomial adjustment. Alternatively, density approximants can be secured by appropriately truncating the distributions or mapping them onto compact supports. The validity of these approaches is corroborated by simulation studies. …