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Copula function is a bridge connecting the marginal and joint distributions of the random variables [21].
The distributions of the random variables for civil engineering structures are provided, and the relative importance of these random variables is determined.
To understand uncertainty in roundabout capacity estimation, the probability distributions of the random variables of the capacity model had to be identified.
Both Pf, and its sensitivity to the parameters of the distributions of the random quantities controlling the system response have been evaluated.
Chance constraints are generally difficult to solve especially when we do not have the full information about the distributions of the random variables due to the fading effects of wireless channels [17, 18].
Often we are concerned with multivariate stochastic modeling and risk analysis of the systems and processes that involve the derivation of probability distributions of the random variables considering the dependence structure among them.
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Numerical examples of two different spatial distributions of the random-in-time forcing function are explored and optimal absorber parameters are presented.
The genome scan was repeated 1000 times with a randomized response vector to obtain an empirical distribution of the random genetic effect under null hypothesis.
Thus, the distribution of the random variable R defined in the preceding section is the function of i = 0, 1,…, n given in the binomial equation.
These results do not depend on the assumption of a Gaussian distribution of the random effects.
An optimal filter depends on the parameters governing the distribution of the random set.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com