论文信息 - DERIVATION OF THE GAMMA DISTRIBUTION BY USING THE PRINCIPLE OF MAXIMUM ENTROPY (POME)

DERIVATION OF THE GAMMA DISTRIBUTION BY USING THE PRINCIPLE OF MAXIMUM ENTROPY (POME)

The principle of maximum entropy (POME) was used to derive the two-parameter gamma distribution used frequently in synthesis of instantaneous or finite-period unit hydrographs. The POME yielded the minimally prejudiced gamma distribution by maximizing the entropy subject to two appropriate constraints which were the mean of real values and the mean of the logarithms of real values of the variable. It provided a unique method for parameter estimation. Experimental data were used to compare this method with the methods of moments, cumulants, maximum likelihood estimation, and least squares.

Vijay P. Singh | Kulwant Singh | Kulwant Singh | V. Singh | Vijay P. Singh

[1] P. W. Jowitt,et al. The extreme-value type-1 distribution and the principle of maximum entropy , 1979 .

[2] J Munro,et al. DECISION ANALYSIS IN THE READY-MIXED CONCRETE INDUSTRY. , 1978 .

[3] J. Dooge. A general theory of the unit hydrograph , 1959 .

[4] V. Yevjevich,et al. Estimation of Skewness of Hydrologic Variables , 1984 .

[5] J. Lienhard. A statistical mechanical prediction of the dimensionless unit hydrograph , 1964 .

[6] James C. I. Dooge,et al. Linear Theory of Hydrologic Systems , 1973 .

[7] J. O. Sonuga. Principle of maximum entropy in hydrologic frequency analysis , 1972 .

[8] J. Nash. Systematic determination of unit hydrograph parameters , 1959 .

[9] M. A. Collins. DISCUSSION.: "Fitting a Gamma Distribution Over a Synthetic Unit Hydrograph", by Gert Aron and Elizabeth L. White , 1983 .

[10] C. T. Haan,et al. Statistical Methods In Hydrology , 1977 .

[11] D. Gray. Synthetic Unit Hydrographs for Small Watersheds , 1961 .

[12] G. Aron,et al. Fitting a Gamma Distribution Over a Synthetic Unit Hydrograph , 1982 .

[13] T. Croley. Gamma synthetic hydrographs , 1980 .

[14] H. Schwarz,et al. Unit-hydrograph lag and peak flow related to basin characteristics , 1952 .

[15] C. E. SHANNON,et al. A mathematical theory of communication , 1948, MOCO.

[16] John H. Lienhard,et al. A physical basis for the generalized gamma distribution , 1967 .