Exact distribution of the linear combination of p Gumbel random variables

The distribution of linear combinations of independent Gumbel random variables arises explicitly in many applied areas, including economics, electrical and electronic engineering, and hydrological sciences. However, the exact distribution has not been known in its most general form. In this paper, the exact distribution of the linear combination Z=α1 X 1+···+α p X p is derived when X j are independent Gumbel random variables. A computer program is provided for the associated percentile points.

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