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Did you look at the Pollaczek–Khinchine transform? The distribution is hypo-exponential, which is simple in the bi-variate case, $$2(exp(-x)-exp(-2x)).$$$$2(\exp(-x)-\exp(-2x)).$$ The Laplace transform of this is simple to find which should enable the Pollaczek–Khinchine transform.

Did you look at the Pollaczek–Khinchine transform? The distribution is hypo-exponential, which is simple in the bi-variate case, $$2(exp(-x)-exp(-2x)).$$ The Laplace transform of this is simple to find which should enable the Pollaczek–Khinchine transform.

Did you look at the Pollaczek–Khinchine transform? The distribution is hypo-exponential, which is simple in the bi-variate case, $$2(\exp(-x)-\exp(-2x)).$$ The Laplace transform of this is simple to find which should enable the Pollaczek–Khinchine transform.

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Did you look at the Pollaczek–Khinchine transform? The distribution is hypo-exponential, which is simple in the bi-variate case, $$2(exp(-x)-exp(-2x)).$$ The Laplace transform of this is simple to find which should enable the Pollaczek–Khinchine transform.