The distributions presented in the figures were obtained with the maximum entropy procedure, unless stated otherwise.
Classic maximum entropy quantile function method (CMEQFM) based on the probability weighted moments (PWMs) can accurately estimate the quantile function of random variable on small samples, but inaccurately on the very small samples.
To overcome this weakness, least square maximum entropy quantile function method (LSMEQFM) and that with constraint condition (LSMEQFMCC) are proposed.
Local maximum entropy shape functions are used which possess a weak Kronecker-δ property.
The numerical results indicate that the proposed Maximum-Entropy Meshless method based on the maximum entropy shape functions is able to provide stable and robust solutions for consolidation problems in porous media.
Equation (12) shows that maximum entropy is a function of Lagrange multipliers and constraints, such that Hmax is a concave function.
This paper studies the maximum entropy probabilistic density function reconstruction method based on cumulant arithmetic of linearized load flow formulation, and then develops a maximum entropy based PLF (ME-PLF) calculation algorithm for power system integrated with wind power generation (WPG).
To determine the maximum value of entropy function, we construct Lagrange's function H (P i,n, R i,j,n, S i,n, D n, V l,n ) by introducing the Lagrange's multipliers θ i (1 ≤ i ≤ k), δ i j (1 ≤ i ≤ k), ϕ i (1 ≤ i ≤ k), θ k + 1, ε l (1 ≤ l ≤ J) and ϕ k + 1 corresponding to the information, i.e. constraints (69 71) available in the form of derived analytical results.
Based on the maximum entropy principle, the cost function of EDP is approximated by using a smooth and differentiable function to improve the performance of the SQP.
Notably, the maximum difference approach significantly outperformed all other methods while increasing the marginal gap as the number of functions increased (P < 9.32 × 10 − 26 relative to maximum entropy for 15 unknown functions).
