Section6 - CEE 304 Section Example Problems 1 The maximum...

Info icon This preview shows pages 1–2. Sign up to view the full content.

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 α, ξ Since, 5 . 2 5772 . 0 = + = α ξ μ X , ( ) 2 2 2 7 . 0 645 . 1 = = α σ X Hence, α = 1.832, ξ = 2.185 p = ( ) ( ) [ ] { } ξ α = p p X x x F exp exp => ξ - ln[-lnp]/ α = p x => x 0.98 = 2.185 – ln(-ln0.98)/1.832 = 4.315 in. Lognormal Distribution: L = ln(X) ~ N ( ) 2 , L L σ μ We can compute 879 . 0 = L μ , 275 . 0 = L σ 0.98 = P ( ) 98 . 0 x X = P ( ) 98 . 0 ln x L = P ( ) L L L L x L σ μ σ μ 98 . 0 ln = ( ) Φ 275 . 0 879 . 0 ln 98 . 0 x From the Normal dist. Table, ( ) 055 . 2 275 . 0
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern