MATH 2009 Engineering Modelling
Practical Questions: Practical 4 (Week 5)
Distributions, Statistical Measures
1. For the first activity, we will need the file MurrayBridgeRainfall.mtw from the website. This is 134
years of monthly rainfall data. We will first fit a Gamma distribution to the rainfall for July. First,
calculate the descriptive statistics for the July rainfall. If you forget how to do this, look back
to Practical 1. Then, use the formulae αβ = x¯ and αβ2 = s2 to find values for the two parameters.
2. Then label column 16 as SyntheticJuly. Go to the Calc menu, then Random Data, and then
Gamma. Select 1000 values to be generated, and then select the column SyntheticJuly, and enter the
parameters you have calculated and hit Ok. As a check you can get the descriptive statistics for this
column as well as the July data to check that everything has gone well.
3. Next go to the Graph menu and select Histogram, Simple and enter the two July columns, data
and synthetic. Go to the link to Multiple Graphs and tick Overlaid on same graph. Then go to the
link Scale, and Y-Scale Type and Density. Comment on what this looks like when you generate the
4. Then go to the Graph menu once more and then Empirical CDF, Single and enter both variables
again. Then make sure they will be overlaid on the same graph, and go to the Distribution link. There
is a drop down menu for what distribution to compare to - select Gamma, and enter the appropriate
parameters in the boxes, and continue. Once again comment on the result.
5. Extra. Repeat using the file of output from a wind farm WattlePoint.mtw.