Question

Level analysis. Researchers have discovered that the maximum flood level (in millions of cubic feet per second) over a 4-year period for the Susquehanna River at Harrisburg, Pennsylvania, follows approximately a gamma distribution with α and β parameters (Journal of Quality Technology, Jan. 1986).

a. Find the mean and variance of the maximum flood level over a 4-year period for the Susquehanna River.

b. The researchers arrived at their conclusions about the maximum flood level distribution by observing maximum flood levels over 4-year periods, beginning in 1890. Suppose that over the next 4-year period, the maximum flood level was observed to be 0.60 million cubic feet per second. Would you expect to observe a value this high from a gamma distribution with α and β parameters? What can you infer about the maximum flood level distribution for the 4-year period observed?

Answer 1

The mean and variance of the maximum flood level over a 4-year period can be found using the parameters α and β of the gamma distribution. To determine if a specific value is expected from the gamma distribution, we compare it to the distribution. Inferences about the maximum flood level distribution can be made based on the likelihood of the observed value.

Step-by-step explanation:

a. To find the mean and variance of the maximum flood level over a 4-year period, we need to use the parameters α and β of the gamma distribution. The mean (μ) of a gamma distribution is α * β and the variance (σ^2) is α * β^2.

b. To determine if a value of 0.60 million cubic feet per second is expected from the gamma distribution, we can compare it to the distribution and see if it falls within a certain range. We can infer about the maximum flood level distribution for the observed 4-year period based on how likely or unlikely the value is in relation to the gamma distribution parameters.