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Unformatted text preview: CEE 304 Section Example Problems (101106) 1. The maximum annual 24hour rainfall in Vermont has a mean of 2.5 inches and a standard deviation of 0.7 inches. The distribution is often described by a Gumbel distribution (the appropriate asymptotic distribution) or the lognormal distribution (a reasonable distribution for describing strictly positive variates). Estimate the 50year (98 th percentile) rainfall depth using both distributions. How far can you get with the gamma distribution? Gumbel Distribution: First want parameters , Since, 5 . 2 5772 . = + = X , ( ) 2 2 2 7 . 645 . 1 = = X Hence, = 1.832, = 2.185 p = ( ) ( ) [ ] { } = p p X x x F exp exp =>  ln[lnp]/ = p x => x 0.98 = 2.185 ln(ln0.98)/1.832 = 4.315 in. Lognormal Distribution: L = ln(X) ~ N ( ) 2 , L L We can compute 879 . = L , 275 . = L 0.98 = P ( ) 98 ....
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 Fall '08
 Stedinger

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