Entropy-Based Parameter Estimation in Hydrology by Vijay P. Singh (auth.)

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By Vijay P. Singh (auth.)

Since the pioneering paintings of Shannon within the overdue 1940's at the improvement of the idea of entropy and the landmark contributions of Jaynes a decade later resulting in the improvement of the primary of utmost entropy (POME), the concept that of entropy has been more and more utilized in a large spectrum of components, together with chemistry, electronics and communications engineering, information acquisition and garage and retreival, info tracking community layout, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, photo processing, administration sciences, operations learn, development attractiveness and identity, photogrammetry, psychology, physics and quantum mechanics, reliability research, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, etc. New components discovering software of entropy have on the grounds that persisted to spread. The entropy suggestion is certainly flexible and its applicability common. within the quarter of hydrology and water assets, various purposes of entropy were stated prior to now 3 a long time or so. This ebook specializes in parameter estimation utilizing entropy for a couple of distributions usually utilized in hydrology. within the entropy-based parameter estimation the distribution parameters are expressed by way of the given details, known as constraints. hence, the tactic lends itself to a actual interpretation of the parameters. as the info to be exact frequently constitutes adequate statistics for the distribution into account, the entropy technique presents a quantitative approach to convey the data inside the distribution.

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1983. Automatic calibration of conceptual rainfall-runoff models: the question of parameter observability and uniqueness. Water Resources Research, Vol. 1, pp. 260-268. K. , 1983. Evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall-runof models: Influence of calibration data variability and length on model credibility. Water Resources Research, Vol. 1, pp. 251-259. , 1985. Regional hydrologic analysis: 1. Ordinary, weighted and generalized least squares compared.

Wang (1996) defined partial PWMs and derived them for extreme value type I and ill distributions. He applied these moments to lower bound censored samples. Let a probability distribution function be denoted as F=F(X)=P[X ,,; xl. 64) where Mjj,k is the probability weighted moment of order (i, j, k), E is the expectation operator and i, j and k are real numbers. o,o represents the conventional moment about origin of order i. o exists and X is a continuous function of F, then M jj •k exists for all nonnegative real numbers j and k.

8 ROBUSTNESS Kuczera (1982a, b, c) defined a robust estimator as the one that is resistant and efficient over a wide range of population fluctuations. Two criteria for resistant estimator are mini-max and minimum average RMSE. According to the mini-max criteria, the maximum RMSE for all population cases should be minimum .. Thus, for a resistant estimator the average RMSE as well as the maximum RMSE should be minimum. 2 .. 232) in which N is sample size, Q is observed quantity of a given probability and Q c is computed quantity of the same probability.

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