Abstract
The classical maximum entropy (ME) problem consists of determining a probability distribution function (pdf) from a finite set of expectations μ n = E {ø n (x)} of known functions ø; n (x), n = 0,…, N. The solution depends on N + 1 Lagrange multipliers which are determined by solving the set of nonlinear equations formed by the N data constraints and the normalization constraint. In this short communication we give three Matlab programs to calculate these Lagrange multipliers. The first considers the case where ø n (x) can be any functions. The second considers the special case where ø n (x) = x n, n = 0,..., N. In this case the µ n are the geometrical moments of p(x). The third considers the special case where ø n (x) = exp(−jnωx), n = 0,..., N. In this case the µ n are the trigonometrical moments (Fourier components) of p(x). We give also some examples to illustrate the usefullness of these programs.
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© 1992 Springer Science+Business Media Dordrecht
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Mohammad-Djafari, A. (1992). A Matlab Program to Calculate the Maximum Entropy Distributions. In: Smith, C.R., Erickson, G.J., Neudorfer, P.O. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2219-3_16
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DOI: https://doi.org/10.1007/978-94-017-2219-3_16
Publisher Name: Springer, Dordrecht
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