Maximum entropy probability distributions for flood frequency analysis

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Abstract
It is customary to assume a frequency distribution in flood frequency analysis. The parameters of the distribution are estimated by using observed or transformed data. The fitted distribution is then used to estimate the magnitudes of floods of different frequencies. The maximum entropy (ME) probability distribution is defined as the 'minimally prejudiced probability distribution which maximizes the entropy subject to constraints supplied by the given information'. In spite of many attractive features of the ME distribution, it has not been used in its general form in practice. The main reason for not using the ME distribution in its general form is that the parameter estimation problem associated with the ME distribution is not easy. Recently this problem has been solved and an algorithm has been developed to estimate the parameters of the ME distribution. The objective of the research reported in the present paper is to fit ME distributions to flood data. The ME distributions are compared with other well known distributions. The computational aspects and selection of orders of distributions are also discussed. The ME distribution is shown to be versatile and fits a variety of flood data very well.