15.8.2. Probability Distributions Used

Try these first

1. 1.

   What is the Gumbel Distribution used for?

   Hint

   Think of extreme values.

2. 2.

   Define the Normal Distribution.

   Hint

   Consider the shape of a bell curve.

3. 3.

   What is the main purpose of using the Gumbel Distribution?

   • Modeling normal rainfall patterns
   • Predicting extreme rainfall events
   • Calculating average rainfall

   Hint

   Recall its connection with flood predictions.

4. 4.

   True or False: The Log Normal Distribution is used when the raw data is normally distributed.

   • True
   • False

   Hint

   Think about the relationship of the data's transformation.

5. 5.

   Using a Gumbel Distribution, forecast the expected maximum rainfall for the next 50 years based on historical data showing maximums of 150 mm, 200 mm, and 250 mm in the past.

   Hint

   Utilize the Gumbel calculations for extreme value prediction based on historical records.

6. 6.

   You have rainfall data logged over 30 years showing a positive skew. Determine when to use the Log Pearson Type III method versus the Normal Distribution.

   Hint

   Always gauge data characteristics before selecting a distribution.