Section6 - CEE 304 Section Example Problems (10-11-06) 1....

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Unformatted text preview: CEE 304 Section Example Problems (10-11-06) 1. The maximum annual 24-hour 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 50-year (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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Section6 - CEE 304 Section Example Problems (10-11-06) 1....

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