FREQUENCY CURVES: TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS OF THE UNITED STATES GEOLOGICAL SURVEY BOOK 4, CHAPTER A2 by H.C. Riggs Prepared by the U.S. Geological Survey TABLE OF CONTENTS Preface Abstract Introduction Cumulative distributions Distributions used in hydrology     Normal distribution     Lognormal distribution     Type I extreme-value distribution (Gumbel)     Type III extreme-value distribution     Pearson Type III distribution     Graphically defined distributions Mathematical curve fitting     Normal distribution     Three-parameter distributions     Type I extreme-value distribution (Gumbel)     Type III extreme-value distribution Graphical fitting     Example of graphical fitting     Use of historical data Comparison of mathematical and graphical fitting Describing frequency curves Interpretation of frequency curves Special cumulative frequency curves References cited FIGURES 1. Graphs showing two normal distributions and their cumulative forms 2. Graphs showing normal and skewed distributions and their cumulative forms on a normal-probability plot 3. Graphs showing relative positions of the mean, median, and mode for right- skewed (upper) and left-skewed (lower) distributions 4. Frequency curves showing effect of direction of skew and direction of cumu- lation on position of the mean with respect to the median 5. Gumbel frequency curve of annual floods on Columbia River near the Dalles, Oreg., showing agreement with the plotted points 6. Frequency curve based on data from table 3, assuming that data are annual maximums 7. Frequency curve based on data from table 3, assuming that data are annual minimums 8. Design-probability curves (lower graphs) and the frequency curve on which they are based (upper graph) 9. Frequency curve of annual minimum flows and plot showing serial correlation, south Fork Obion River near Greenfield, Tenn. TABLES 1. Frequency factors for Pearson Type III distribution 2. Means and standard deviations of reduced extremes 3. Computation of plotting position ABSTRACT This manual describes graphical and mathematical procedures for preparing frequency curves from samples of hydrologic data. It also discusses the theory of frequency curves, compares advantages of graphical and mathematical fitting, suggests methods of describing graphically defined frequency curves analytically, and emphasizes the correct interpretations of a frequency curve. LizardTech's Djvu plug-in is needed to view these reports. CLICK HERE TO VIEW THE ENTIRE REPORT For questions or comments, contact K. Van Wilson.