COMPUTATIONS--New Computer Program (K957) for Pearson Type III Frequency Analysis




In Reply Refer To:                                               May 30, 1980
WGS-Mail Stop 415




SURFACE WATER BRANCH TECHNICAL MEMORANDUM NO. 80.05

Subject:  COMPUTATIONS--New Computer Program (K957) for Pearson Type III
                       Frequency Analysis

A new computer program K957 by W. Kirby fits a Pearson Type III distribution
to natural values of hydrologic data without first transforming the data
to logarithms.  This program may prove useful when analyzing the frequency
of such hydrologic data as annual low flows, annual lake or tidal elevations,
or various annual water-quality data.  As in all frequency analyses, judgments
and assumptions are required for fitting and using the distribution.

The program fits a Pearson Type III distribution to random data values using
the method of moments.  The mean, standard deviation, and skewness of the
input sample are first determined and a Pearson Type III distribution
computed.  No logarithmic transformation of the input data is performed.
An option exists to replace the computed sample skew with a user-specified
value.  Program output includes listing of input data with Weibull plotting
of confidence limits for the 5 and 95 level of significance, and a line
printer plot of the fitted curve and data points.

The Fortran program is structured such that computations, the input, output,
and editing of the data are performed in separate subroutines.  The main
program, which calls the subroutines, can be easily modified by the analyst
to allow for a variety of transformations to the input data.

The input data are prepared in the card-image format described in the WATSTORE
User's Guide, v. 4, chap. I, section C.2.k., August 1979.  This is the same
format required for the stand-alone operation (card input) of program J407
for analyzing annual flood-peak data by Water Resources Council Bulletin 17A
Guidelines.  Differences in J407 and K957 other than the log transform are
that K957 (1) ignores the gage base discharge and all historic or outlier
specifications, and (2) does not weight sample and generalized skews.  K957
uses either the computed sample skew or the skew specified in columns 58-62
of the station name card.  If a user-specified skew is to be used in the
analysis, the letter G must be coded in the station-option code field
(columns 63-67) of the station name card.







                                                                       Page 2

The program which is available on RE1, 2, or 3 can be executed with the
following statements:

      /*RELAY  PUNCH REn   (n = 1, 2, or 3)

                                 (job card)

      // EXEC FORTRUN,PROG=K957
     //GO.SYSIN DD *

                              (input data cards)

    /*
    //
    $$$

Any questions or problems concerning this program should be directed to
W. O. Thomas in the Surface Water Branch (FTS 928-6837).




                                       Harry H. Barnes, Jr.
                                       Chief, Surface Water Branch

"This memorandum does not supersede any existing WRD memorandum."

WRD Distribution:  A, B, S, FO, PO