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  5. Optimal approximation of density function by minimum information loss criterion

Optimal approximation of density function by minimum information loss criterion

V. Dubnitskiy, I. Skorikova, A. Khodyrev
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A method proposed for approximation quality estimate of probability distribution density using Kullback divergence. The proposed measure of density function approximation quality is the value of Kullback divergence which is determined relative to distribution to be approximated over the totality of approximating functions. Expressions found for determination of Kullback divergence for pairs of truncated distributions. Application of the method is shown by solution of optimal approximation selection problem for truncated normal distribution among the following distributions: Laplace distribution, double exponential distribution, logistic distribution, Champernowne distribution, gamma distribution, lognormal distribution. After a numerical experiment it was found that the best normal distribution interpolation at selected truncation interval ( ) will be lognormal distribution. The obtained result serves as experimental confirmation of the previous assumption that lognormal distribution quite well approximates normal distribution provided its coefficient of variation is v<0,25. 280 x 320 
Keywords: approximation of probability distribution density, Kullback divergence, truncated distributions, Laplace distribution, double exponential distribution, logistic distribution, Champernowne distribution, gamma distribution, lognormal distribution