Download Frequency Analysis Histogram

Usefulness of Frequency Analysis
Frequency Analysis
T. Giambelluca
GEOG 405
University of Hawai‘i at Mānoa
Histogram
• Determine high and low
values
• Divide the range into a
reasonable number of
“bins”
• Count the number of
values in each bin
• Convert counts to relative
frequency (optional)
• Plot using a column chart
By analyzing the frequency of past events,
we can estimate the probability of future
events.
We often assume:
Probability (future) = Frequency (past)
Probability Density Functions
(PDFs)
• The histogram can be
represented by a smooth
curve
• A theoretical probability
density function (pdf) can
be “fitted” to the data
• For example, the normal
distribution function often
fits annual rainfall data
very well (right)
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Probability Density Functions
• The normal distribution
can be adjusted to the
sample by changing the
values of its two
parameters: mean and
variance
Variance = (Std. Dev.)2
Y=
Probability Density Functions
Annual rainfall is often normally distributed. But, shorter
interval rainfall data are usually skewed, with a high
frequency of low values. For example, daily rainfall (below).
Probability Density Functions
• Use of a PDF allows
probabilities to be
calculated for any range
of values
• For example, if a data set
is normally distributed,
the probability of a value
occurring in the range of
one standard deviation
below and above the
mean is 68%
Probability Density Functions
• Gamma distribution is
useful for skewed
samples
Y=
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Extreme Value Analysis
• In hydrology, we are often
more interested in the
extreme values than the
middle of the distribution
• Special functions are used
to estimate the extremes of
a distribution
• The generalized extreme
value (GEV) distribution
includes several distinct
types, including the Gumble
distribution
Extreme Value Analysis
Extreme Value Analysis
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Partial Duration Series:
ranked list of highest values in
a sample
Annual Maximum Series:
ranked list of the highest
values recorded in each year
of record
Duration: time interval of data
series
Rank (m): position in ordered
series
Sample Size (n): number in
sample
Exceedance Frequency (f):
Return Period (RP):
f =
m
n +1
RP =
1 n +1
=
f
m
Extreme Value Analysis
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Extreme Value Analysis
Extreme Value Analysis
Extreme Value Analysis
Extreme Value Analysis
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Extreme Value Analysis
• Point-to-Area Problem
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