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A maximum entropy distribution signifies the decentralization of the network.
However, for continuous models the maximum entropy distribution depends crucially on the metric over the parameters in the model.
A trivariate maximum entropy distribution of significant wave height, wind speed and the relative direction is proposed here.
Kemp (2006) presented a discrete half normal distribution as a maximum entropy distribution for given mean and variance with support 0, 1, 2 ⋯.
Applying the Lagrange Euler calculus of variation, Eq. (4) leads to the maximum entropy distribution: f(x) = exp left[ { - ;sumlimits_{i = 0}^{m} {lambda_{i} g_{i} (x)} } right].
The corresponding sampling data about significant wave heights, wind speeds and the relative directions from a location in the North Atlantic is applied for statistical analysis, and the results show that the trivariate maximum entropy distribution is sufficiently good to fit the data, and method of conditional probability can reduce the design values efficiently.
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Based on copulas and univariate maximum entropy margins, multivariate maximum entropy distributions are constructed.
In this joint distribution, all the marginal variables follow modified maximum entropy distributions, and they are combined by a correlation coefficient matrix based on the Nataf transformation.
In this paper, the bounded information on statistical moments is used to construct a family of Maximum Entropy distributions, leading to an uncertain probability function.
The marginal fittings of univariate maximum entropy distributions and the trivariate data fitting based on normal copula fit the data well.
The training procedure is performed by iterating through three steps: computing sufficient statistics, training all maximum entropy distributions, and calculating occupation probabilities.
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