Generation of correlated parameters for statistical circuit simulation

Standard transformations for converting non-Gaussian raw data to the Gaussian domain are reviewed. Once the appropriate transformation is determined, conversion formulas are developed so that only the raw data's mean and variance are required to convert any future data points to the Gaussian domain. With the input parameters represented in terms of the Gaussian distribution, techniques from multivariate statistics are used to generate statistically correlated sets of parameters. The method used to generate input parameters for Monte Carlo simulations is examined. The technique is based on the relatively easy generation of statistically independent observations and their relationship to the more general case of statistically dependent observations by way of the parameters' correlation matrix. A method called deterministic tracking of model parameters is developed. Using the definition of an isodensity contour for a p-variate normal density function, an expression is derived to calculate the most probable setting of input parameters, given that a subset of these parameters was first fixed to specific values. A simple but realistic three-variable example of the methods developed is shown.<
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