Statistics for Environmental Engineers

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50.3    Uniform Distribution. Data from a process is discovered to have a uniform distribution with mean 10 and range 2. Future samples from this process will be of size n = 10. By simulation, determine the reference distribution for the standard deviation, the standard error of the mean, and the 95% confidence interval of the mean for samples of size n = 10.


50.4    Regression. Extend the example in Table 50.3 and add five to ten more points to Figure 50.3.


50.5    Bootstrap Confidence Intervals. Fit the exponential model у = в1 exp(-02 x) to the data below and use the bootstrap method to determine the approximate joint confidence region of the parameter estimates.


x 1    4    8    10    11


y    179    104    51    35    30


Optional: Add two observations (x = 15, у = 14 and x = 18, у = 8) to the data and repeat the bootstrap experiment to see how the shape of the confidence region is changed by having data at larger values of x.


50.6    Legal Statistics. Find an unfamiliar or unusual statistic in a state or U.S. environmental regulation and discover its properties by simulation.


50.7    99th Percentile Distribution. A quality measure for an industrial discharge (kg/day of TSS) has a lognormal distribution with mean 3000 and standard deviation 2000. Use simulation to construct a reference distribution of the 99th percentile value of the TSS load. From this distribution, estimate an upper 90% confidence limit for the 99th percentile.

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Introduction to Time Series Modeling


KEY WORDS ARIMA model, ARMA model, AR model, autocorrelation, autocorrelation function, autoregressive model, cross-correlation, integrated model, IMA model, intervention analysis, lag, linear trend, MA model, moving average model, nonstationary, parsimony, seasonality, stationary, time series, transfer function.

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