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arXiv · 1203.3288

Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density

Zhong Zheng·Lu Wei·Jyri Hämäläinen·Olav Tirkkonen
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Abstract

We derive a closed-form expression for the orthogonal polynomials associated with the general lognormal density. The result can be utilized to construct easily computable approximations for probability density function of a product of random variables, when the considered variates are either independent or correlated. As an example, we have calculated the approximative distribution for the product of Nakagami-m variables. Simulations indicate that accuracy of the proposed approximation is good with small cross-correlations under light fading condition.

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Zhong Zheng, Lu Wei, Jyri Hämäläinen, Olav Tirkkonen. 2012-03-15. Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density. https://doi.org/10.1109/lcomm.2012.101712.122141

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