Annual maximum hourly rainfall data at 689 raingages in California was analysed by the State of California ["Rainfall depth-duration-frequency for California", Technical Report, State of California Department of Water Resources, 1981]. It was suggested that a gamma distribution was appropriate for the data because the average values of sample skewness and kurtosis were consistent with the relationship between the population skewness and kurtosis of gamma distributions. This inference is valid only if sample moments are accurate estimators of population moments. For the California data, this is dubious, because the sample sizes are small -- only 12 gauges have records as long as 50 years. L-moments tell a different story.
The sample L-skewness and L-kurtosis
values for the 68 sites with at least 20 years
of record in the Central Valley of California are shown in
the first diagram.
The data are on average closer to the population L-moments of a
generalized extreme-value (GEV)
distribution rather than a gamma distribution.
The second diagram shows sample L-moments of data simulated from
independent GEV distributions each with population L-skewness 0.24
(the average of the 68 sample L-skewness values)
and the same record lengths as the actual rainfall records.
The scatter of the points is similar to the first diagram.
This is what one would expect if the
actual data did in fact follow a GEV distribution.
Sample L-moments of data simulated from a gamma distribution are shown
in the third diagram. This has an appearance rather different from
the first two diagrams: there are many fewer points above the "GEV"
line and many more below the "gamma" line.
We therefore conclude that the Central Valley hourly rainfall data may be well described by a GEV distribution but seem most unlikely to follow a gamma distribution.
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