Abstract
This chapter aims to build intuition about probability density functions (PDFs), Monte Carlo sampling, and yield estimation. It has an emphasis on graphical analysis as opposed to equations. Such intuition will help in many design scenarios, when one is observing actual PDF data in the form of scatterplots, histograms, and normal quantile (NQ) plots.
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Notes
- 1.
For further clarification: Two identically distributed distributions have exactly the same distribution shape (e.g., normal) and distribution parameters (e.g., same mean and standard deviation). Two “independently distributed” distributions have no correlation with each other; if we have a value for one distribution, that value does not change what the probable values for the other distribution might be.
- 2.
In the statistics literature, “Monte Carlo methods” are a broad set of algorithms, where the unifying element is that each algorithm has some randomization. While we use the label “sample” to mean a single point in process variable space drawn from a distribution or its corresponding output performance values, in the statistics literature such a point is an “observation” and a “sample” is a set of observations. The circuits community tends to use “sample” in the way we do.
- 3.
We agree, the terminology is somewhat confusing!
- 4.
CDF = Cumulative Distribution Function. CDF(x) is the area under the PDF from −∞ to x.
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McConaghy, T., Breen, K., Dyck, J., Gupta, A. (2013). A Pictorial Primer on Probabilities. In: Variation-Aware Design of Custom Integrated Circuits: A Hands-on Field Guide. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2269-3_3
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DOI: https://doi.org/10.1007/978-1-4614-2269-3_3
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