By J. N. Kapur, H. K. Kesavan (auth.), V. P. Singh, M. Fiorentino (eds.)
Since the landmark contributions of C. E. Shannon in 1948, and people of E. T. Jaynes a few decade later, purposes of the concept that of entropy and the main of extreme entropy have proliterated in technological know-how and engineering. fresh years have witnessed a extensive variety of recent and intriguing advancements in hydrology and water assets utilizing the entropy proposal. those have encompassed cutting edge equipment for hydrologic community layout, move of knowledge, circulate forecasting, reliability review for water distribution platforms, parameter estimation, derivation of chance distributions, drainage-network research, sediment yield modeling and pollutant loading, bridge-scour research, building of pace profiles, comparative assessment of hydrologic versions, etc. a few of these tools carry nice promise for development of engineering perform, allowing rational choices to standard methods. however, the innovations of strength and effort dissipation are being more and more utilized to a large spectrum of difficulties in environmental and water assets. either entropy and effort dissipation have their foundation in thermodynamics, and are comparable ideas. but, a few of the advancements utilizing entropy appear to be dependent solely on statistical interpretation and feature probably little actual content material. for instance, lots of the entropy-related advancements and purposes in water assets were in keeping with the information-theoretic interpretation of entropy. We think if the facility of the entropy idea is to be totally learned, then its actual foundation should be established.
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Singh (1987a) estimated, using POME, the parameters of the extreme-value type III distribution and found the POME-based method better than the methods of moments and maximum likelihood estimate. In other comparative studies, the POME-based method was found to be superior to or as good as the best of the other methods. , 1990b). Singh and Rajagopal (1987) used POME to develop a new parameter-estimation method, called parameter-space expansion method, which is applicable to any probability distribution with any number of parameters that is expressible in direct form.
1 DERIVATION OF HYPOTHESES The POME-based method gives rise to the best estimate of a probability distribution taking account of all the available infonnation. If the available infonnation is changed then the estimate will also be changed. The methodology is very general and applicable to analysis of different systems, and the range of possible application for deriving hypotheses (or estimating the fonn of system models) is very wide indeed. For a wide class of problems marked by their complexity, the methodology provides a set of rules for model construction compatible with the given infonnation, and an internal consistency not easily achievable otherwise.
Building on these investigations, Singh, et al. (1985, 1986) derived a number of distributions. A derivation of the extremevalue type III distribution for analysis of low f10ws is reported by Singh (1987a). Examples demonstrating application of POME to the log-Gumbel and Wei bull distributions are reported by Singh (1986, 1987b), and to the gamma, Pearson-type III, lognormal, and the log-Pearson type III distributions are described by Singh and Singh (1985a, 1985b, 1985c, 1987,1988). Krstanovic and Singh (1987) extended the POME-based method to multivariate frequency distributions.