With the aid of a linear decision rule, reservoir management and design problems often can be formulated as easily solved linear programing problems. The linear decision rule specifies the release during any period of reservoir operation as the difference between the storage at the beginning of the period and a decision parameter for the period. The decision parameters for the entire study horizon are determined by solving the linear programing problem. Problems may be formulated in either the deterministic or the stochastic environment.

Estimates of flood flows having given recurrence intervals or probabilities of exceedance are needed for design of hydraulic structures and floodplain management. Program PEAKFQ provides estimates of instantaneous annual peak flows having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (exceedance probabilities of 0.50, 0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002, respectively). As implemented in program PEAKFQ, the Pearson Type III frequency distribution is fit to the logarithms of instantaneous annual peak flows following Bulletin 17B guidelines of the Interagency Advisory Committee on Water Data. The parameters of the Pearson Type III frequency curve are estimated by the logarithmic sample moments (mean, standard deviation, and coefficient of skewness). This documentation provides an overview of the computational procedures in program PEAKFQ, provides a description of the program menus, and provides an example of the output from the program.

Some puzzling results from a computer simulation study are explained by showing that the sample skew coefficient has population‐independent bounds depending only on the sample size. Similar results are obtained for the coefficient of variation of positive data, the maximum standardized deviate, and the standardized range. The upper bounds of these statistics are (n − 2)/(n − 1)1/2, (n − 1)1/2, (n − 1)1/2, and (2n)1/2.

The modification in this paper of the familiar Wilson-Hilferty transformation has exactly the same mean, variance, skew, and lower bound as the Pearson type 3 variate that it is intended to approximate. Although the original Wilson-Hilferty approximation is adequate only at skews of less than about. 3.0, the new one remains satisfactory throughout the range of hydrologic interest. Random sampling from skewed probability distributions can be used in the analysis of water resource systems ranging from multipurpose reservoirs to hydrologic data networks. In many of these applications of gamma, or Pearson type 3, distribution, especially its approximate implementation by the Wilson and HiUerty [1931] formula, has become preeminent [e.g., Fiering and Jackson, 1971, p. 53; Matalas, 1967, p. 938]. McMahon and Miller [1971] have found, however, that simulation models using the Wilson-Hilferty approximation cannot reproduce the observed statistical moments of highly skewed hydrologic variables. Some inkling of this problem may be seen in the mathematical form of the approximation, where W is the standardized Wilson-Hilferty variate with the nominal skew •, and C is the standardized normal variate. As the nominal

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