Exact and Near-Exact Distribution of Positive Linear Combinations of Independent Gumbel Random Variables
نویسندگان
چکیده
We show that the exact distribution of a positive linear combination of independent Gumbel random variables can be written as the sum of a linear combination of independent log Gamma distributions, and an independent shifted Generalized Integer Gamma distribution. Given the complexity of this exact distribution, we develop a near-exact distribution using a shifted Generalized Near-Integer Gamma distribution. Our numerical studies confirm the quality of this near-exact approximation as assessed by a proximity measure often used in related studies.
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