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# In a parametric surface point pi is defined by its

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Unformatted text preview: nuities in the estimated density function indicate lack of sampling in corresponding deviation regions. 3.1. Density function of geometrical deviations Using equation (5), geometrical deviation in the manufactured surface can be assumed as a one-dimensional continuous random variable, e. Estimation of the probability density function fundamentally relies on the fact that the probability Pr that a given deviation ei will fall in a region R is given by: Pr (ei ∈ R ) = ∫ f (e)de R (6) where f(e) is the probability density function of the geometrical deviation. The Parzen windows method is a nonparametric method of estimating a probability density function using kernel functions [Parzen, 1962]. Parzen windows estimate the probability density function based on the weighted average of potentially every single sample point; although, only those falling within the selected region have any significant weight. For a one-dimensional variable, regions can be represented by widows with a constant length of h, which are centered at any arbitrary value of e. The p...
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