Skip to main content

Fitting Generalized Gaussian Distributions for Process Capability Index

  • Conference paper
  • First Online:
  • 696 Accesses

Part of the book series: Mathematics in Industry ((TECMI,volume 28))

Abstract

The design process of integrated circuits (IC) aims at a high yield as well as a good IC-performance. The distribution of measured output variables will not be standard Gaussian anymore. In fact, the corresponding probability density function has a more flat shape than in case of standard Gaussian. In order to optimize the yield one needs a statistical model for the observed distribution. One of the promising approaches is to use the so-called Generalized Gaussian distribution function and to estimate its defining parameters. We propose a numerical fast and reliable method for computing these parameters.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Beelen, T.G.J., Dohmen, J.J.: Parameter estimation for a generalized Gaussian distribution. CASA Report 15-40, TU Eindhoven (2015). http://www.win.tue.nl/analysis/reports/rana15-40.pdf

  2. Bombrun, L., Pascal, F., Tourneret, J.-Y., Berthoumieu, Y.: Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions. In: Proceedings of ICASSP-2012, IEEE. International Conference on Acoustics, Speech, and Signal Processing, Kyoto, pp. 3525–3528 (2012). https://hal.archives-ouvertes.fr/hal-00744600

  3. González-Farías, G., Domínguez-Molina, J.A., Rodríguez-Dagnino, R.M.: Efficiency of the approximated shape parameter estimator in the generalized Gaussian distribution. IEEE Trans. Veh. Technol. 58(8), 4214–4223 (2009)

    Article  Google Scholar 

  4. Kokkinakis, K., Nandi, A.K.: Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling. Signal Process. 85, 1852–1858 (2005)

    Article  Google Scholar 

  5. Krupiński, R.: Approximated fast estimator for the shape parameter of generalized Gaussian distribution for a small sample size. Bull. Pol. Acad. Sci. Tech. Sci. 63(2), 405–411 (2015)

    MathSciNet  Google Scholar 

  6. Krupiński, R., Purczyński, J.: Approximated fast estimator for the shape parameter of generalized Gaussian distribution. Signal Process. 86, 205–211 (2006)

    Article  Google Scholar 

  7. Martinez, W.L., Martinez, A.R.: Computational Statistics Handbook with Matlab. Chapman & Hall/CRC, London (2002)

    MATH  Google Scholar 

  8. ter Maten, E.J.W., Wittich, O., Di Bucchianico, A., Doorn, T.S., Beelen, T.G.J.: Importance sampling for determining SRAM yield and optimization with statistical constraint. In: Michielsen, B., Poirier, J.-R. (eds.): Scientific Computing in Electrical Engineering SCEE 2010. Series Mathematics in Industry, vol. 16, pp. 39–48. Springer, Berlin (2012)

    Google Scholar 

  9. Temme, N.M.: Computational aspects of incomplete gamma functions with large complex parameters. Int. Ser. Numer. Math. 119, 551–562 (1994)

    MathSciNet  MATH  Google Scholar 

  10. Wikipedia: Generalized Normal Distribution. https://en.wikipedia.org/wiki/Generalized_normal_distribution; Gamma function. https://en.wikipedia.org/wiki/Gamma_function; Digamma function. https://en.wikipedia.org/wiki/Digamma_function; Incomplete Gamma Function. https://en.wikipedia.org/wiki/Incomplete_gamma_function (2016)

Download references

Acknowledgements

The authors acknowledge support from the projects CORTIF (http://cortif.xlim.fr/): Coexistence Of Radiofrequency Transmission In the Future, a CATRENE project (Cluster for Application and Technology Research in Europe on NanoElectronics, http://www.catrene.org/) and nanoCOPS (http://fp7-nanocops.eu/): Nanoelectronic COupled Problems Solutions, FP7-ICT-2013-11/619166.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. Jan W. ter Maten .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Beelen, T.G.J., Dohmen, J.J., ter Maten, E.J.W., Tasić, B. (2018). Fitting Generalized Gaussian Distributions for Process Capability Index. In: Langer, U., Amrhein, W., Zulehner, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-75538-0_16

Download citation

Publish with us

Policies and ethics