#Confidence interval for MoM estimator of Laplace-distribution´s scale parameter

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sullen hill
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I'm using pivotal method. The Rvs follow a Laplace(0, sigma) distribution. I already found that the distribution of Xi^2 is Weibull (sigma^2, 1/2), but the sum of Weibull Rvs doesn´t follow a known distribution, I tried finding the distribution of the sum with the method of moments generating function without success. Any ideas about how to continue?

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