1,145 research outputs found
Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density
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.Comment: submitted to IEEE Communications Lette
Parameter Identification in a Probabilistic Setting
Parameter identification problems are formulated in a probabilistic language,
where the randomness reflects the uncertainty about the knowledge of the true
values. This setting allows conceptually easily to incorporate new information,
e.g. through a measurement, by connecting it to Bayes's theorem. The unknown
quantity is modelled as a (may be high-dimensional) random variable. Such a
description has two constituents, the measurable function and the measure. One
group of methods is identified as updating the measure, the other group changes
the measurable function. We connect both groups with the relatively recent
methods of functional approximation of stochastic problems, and introduce
especially in combination with the second group of methods a new procedure
which does not need any sampling, hence works completely deterministically. It
also seems to be the fastest and more reliable when compared with other
methods. We show by example that it also works for highly nonlinear non-smooth
problems with non-Gaussian measures.Comment: 29 pages, 16 figure
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