The Interplay between I-max, I-min, p-max and p-min Stable Distributions

Extreme value laws are limit laws of linearly normalized partial maxima of independent and identically distributed (iid) random variables (rvs), also called as l-max stable laws. Similar to l-max stable laws, we have the l-min stable laws which are the limit laws of centered and scaled partial minima, p-max and p-min stable laws which are respectively the limit laws of normalized maxima and minima under power normalization. In this article, we look at transformations between l-max, l-min, p-max and p-min stable distributions and their domains. The transformations in this article are useful in simulation studies.