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CE
397 Statistics in Water Resources
Exercise
2
Frequency
and Probability Distributions
By: David Maidment
Center for
Research in Water Resources
University=
of
Texas at Austin
February 2=
009
I have prepared an Excel Distribution Spreadsheet template=
for
exploring the fitting of probability distributions using the normal and
lognormal distributions for mean annual flows of the Colorado River at Aust=
in
from 1950 to 2008 as an example. These
data are those derived in Exercise 1 of the course using HydroExcel’s
capacity to make annual summaries of daily data, and I have verified that t=
hese
values are consistent with those determined directly from the USGS annual f=
lows
web site.
This spreadsheet is at: http://www.ce.utexas.edu/prof/maidment/StatWR2009/Ex2/ColoFlowDist.xls=
It uses the Excel Toolpak
addin, so you’ll need to have this operat=
ional
on your computer: http://www.ce.utexas.edu/prof/maidment/StatWR2009/Ex1/E=
x1HydroExcel.mht#_Toc221013181
This Distribution Spreadsheet has fo=
ur
tabs in it:
1.&=
nbsp;
Take the last 10 years of the Colorado River flows, 1999 to 2008 and
compute by hand or with a hand-developed spreadsheet using the summation
formulas (not the internal Excel functions) the mean, standard deviation,
variance, median, coefficient of skewness and
standard error of estimate of these data. Verify that your results are
consistent with those produced by the Descriptive Statistics tool in Excel.=
To be turned in: A printout of your results and
computations.
2.&=
nbsp;
Use HydroExcel or other means to find an=
other
data series of interest to you and set up the Distribution Spreadsheet for =
these
data. Do they fit the n=
ormal
or lognormal distributions? W=
rite a
little story about your data – where do they come from? What did you expect to see before =
you
analyzed them? What did you find out once your analysis was complete?
You can get precipitation data from =
http://lwf.nc=
dc.noaa.gov/oa/climate/climatedata.html
Instructions on how to use this web site are at: =
http://www.ce.utexas.edu/prof/maidment/gradhydro2005/docs/ncdcdata.doc=
To be turned in: A printout or screen shot of all p=
ages
of your spreadsheet.
3.&=
nbsp;
Calculate the mean, standard deviation and variance of a random vari=
able
X, whose distribution is uniform from 0 to 1.
4.&=
nbsp;
Use the Analysis Toolpak function Random
Number Generation
to