Chitkara University Publications

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.


  • S Ravi, Department of Studies in Statistics, University of Mysore, Manasagangotri, Mysuru-570006, India
  • TS Mavitha, Department of Studies in Statistics, University of Mysore, Manasagangotri, Mysuru-570006, India



l-max stable laws, l-min stable laws, p-max stable laws, p-min stable laws, domains of attraction


Castillo, E. (1988). Extreme Value Theory in Engineering. Academic Press, San Diego, California.

Christoph, G. and Falk, M. (1996). A note on domains of attraction of p-max stable laws. Stat. Probab. Lett., 37, 279-284.

de Haan, L. and Ferreira, A. (2006). Extreme Value Theory – An introduction. Springer.

Embrechts, P., Klüppelberg, C., and Mikosch, T. (1997). Modeling Extremal Events. Springer-Verlag, Berlin.

Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics, Wiley, New York.

Kotz, S and Nadarajah, S. (2000). Extreme value distributions-Theory and Applications, Imperial College Press, London.

Mohan, N.R, and Ravi, S. (1993). Max domains of attraction of univariate and multivariate p-max stable laws. Theory Probab. Appl. 37, No.4, Translated from Russian Journal, 632-643.

Pancheva, E. (1984). Limit theorems for extreme order statistics under nonlinear normalization, In Stability Problems for Stochastic Models (Lecture Notes in Math.), Springer, Berlin, 1155, 284-309.

Resnick, S.I. (1987). Extreme Values, Regular Variation, and Point Processes, Springer-Verlag, New York.



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