please #3 For the following tasks, use the data set (Q) of USGS 04208000 Cuyahog

Question

please #3

For the following tasks, use the data set (Q) of USGS 04208000 Cuyahoga River at Independence, OH posted in Black Board. Fill out the following table for frequency analysis using various probability density functions. For the Problems from 2 to 5, use the tables of normal distribution or K(Cs, T) in handout (or textbook) and clearly write your skewness coefficient values, such as z or K(Cs, T) if required. Example: z = 2.55 or K(02, 100) = 2.472. Assume that Q follows a Normal distribution, estimate the following. Peak flow of the 100-year return period Peak flow of the 50-year return period Probability that Q is lessthanorequalto 20000 efs Return period of Q = 20000 cfs Same as Problem 2 but use a Log Normal distribution (use natural log) Same as Problem 2 but use a Gamma distribution. Same as Problem 2 but use a Log Pearson Type 3 distribution. For same data set (Q) used in previous problems. Compute and plot the empirical cdf (Weibull) overlaid F(X) values computed by Normal and Log Normal distribution. It is recommended to use Excel for this task. X-axis is Q and Y-axis is the circulative distribution (from 0 to 1). Excel functions) F(X) = NORM.DIST(X, x bar, S_x, cumul = true) F(y) = NORM.DIST(y, ybar, S_y, cumual = true), where y = In(x). Perform the K-s test for a significant level (alpha) 5%. (a) What are the maximum deviation values (|D|) of two cdfs? (b) What is the value of KS for alpha = 5%? (c) Which distribution(s) is (are) accepted?

Explanation / Answer

Problem 3- Here Q is log normal distribution.

So all Q values to be taken as ln(Q) i.e. natural log of Q to be taken and procedure used in problem 2 to be followed but value of Q will be ln(Q)

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