DEPARTMENT OF THE ARMY
U.S. Army Corps of Engineers
Washington, DC 20314-1000
31 October 1997
Engineering and Design
UNCERTAINTY ESTIMATES FOR
NONANALYTIC FREQUENCY CURVES
e. Press, W. H., Flannery, B. P. , Teukosky, S. A.,
and Vettering, W. T. (1990). Numerical Recipes
(Fortran). Cambridge University Press, New York,
This letter presents a methodology for computing the
uncertainty about nonanalytic frequency curves. This
situation arises when estimating flow-frequency curves
1-4. Distribution Statement
and stage-frequency curves. The method involves the
application of order statistics to compute the
Approved for public release, distribution is unlimited.
1-5. Uncertainty Estimation
This letter applies to all HQUSACE elements and
USACE commands where estimates of uncertainty
(1) The uncertainty in a frequency curve that is
about nonanalytic frequency curves are required. The
estimated from a graphical fit of ordered observations
primary expected application is in developing
(e.g., peak annual regulated flows or stages) may be
uncertainty relationships for use in risk-based analysis
calculated from order statistics. No assumption need
of flood damage reduction projects.
be made concerning the analytic form of the frequency
curve. Under these circumstances, the statistic derived
to estimate uncertainty is termed "nonparametric" or,
more to the point, "distribution free." Note that the
a. EM 1110-2-1619. Risk-Based Analysis for
procedures outlined in EM 1110-2-1619, Section 4,
Flood Damage Reduction Studies.
should be utilized if an analytic distribution such as
the log-Pearson III can be used to approximate the
b. Dixon, W. J., and Massey, F. J., Jr. (1957).
Introduction to Statistical Analysis. McGraw Hill,
New York, 488 pp.
(2) The order statistic approach is limited to
calculating uncertainty in the estimated frequency
c. Kottegoda, N. T. (1980). Stochastic Water
curve for the range of observed data or, alternatively,
Resources Technology. Halsted Press, New York,
the equivalent length of record. Extrapolating the
estimates beyond the range of data is performed by
using asymptotic approximations of uncertainty
d. Mood, M. A., Graybill, F. A., and Boes, D. C.
distributions. The order statistic and asymptotic
(1963). Introduction to the Theory of Statistics.
estimates of uncertainty are matched at the limits of
McGraw-Hill, New York, 564 pp.
the observed data.