Skip to main content
SpringerLink
Log in

Efficient determination of a finite set of states for an up-and-down process possessing a practical closure

  • Published:
Automatic Control and Computer Sciences Aims and scope Submit manuscript

Abstract

Conditions at which the up-and-down process with a step greater than 0.5 of the standard deviation of masking noise becomes practically closed on a finite set are investigated, e.g., the sufficient number of states of up-and-down process is determined so that the probability of obtaining other states is practically equal to zero. For this purpose, several lemmas on growth of the cumulative distribution function of standard normal distribution are proved. Formulas for a recursive calculation of the probability of obtaining the state of up-and-down process are obtained. Using them, an upper bound for obtaining other up-and-down process states is given.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Endo, M. and Hayamizu, K., Analysis of standard deviation obtained by up and down method, Electr. Eng. Jpn., 1986, vol. 106, no. 2, pp. 38–45.

    Article  Google Scholar 

  2. Hao, W.D. and Jenq, Y.C., Waveform estimation with jitter noise using stochastic up and down method, IEEE Trans. Instrum. Meas., 1994, vol. 43, no. 2, pp. 200–203.

    Article  Google Scholar 

  3. Stylianou, M., Proschan, M., and Flournoy, N., Estimating the probability of toxicity at the target dose following an up-and-down design, Stat. Med., 2003, vol. 22, no. 4, pp. 535–543.

    Article  Google Scholar 

  4. Lorencs, A., Digital signal processing UD method and its statistical characteristics, Electron. Electr. Eng., 2008, no. 6, pp. 33–36.

    Google Scholar 

  5. Kruminsh, K., Lorencs, A., and Plocinsh, V., Mathematical abstractions and practical realization of the “upand-down” method, Autom. Control Comput. Sci., 2010, vol. 44, no. 4, pp. 191–198.

    Article  Google Scholar 

  6. Krumin'sh, K., Peterson, V., and Plotsinsh, V., The influence of thermal hysteresis of a clocked comparator on the operation of the comparator type sampling converter, Autom. Control Comput. Sci., 2015, vol. 49, no. 4, pp. 245–253.

    Article  Google Scholar 

  7. Dumbgen, L., Bounding Standard Gaussian Tail Probabilities, Technical Report no. 76 of University of Bern, Institute of Mathematical Statistics and Actuarial Science, 2010.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Electronics and Computer Science, Riga, LV-1006, Latvia

    A. Lorencs & V. Plocins

Authors
  1. A. Lorencs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Plocins
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Plocins.

Additional information

The article is published in the original.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lorencs, A., Plocins, V. Efficient determination of a finite set of states for an up-and-down process possessing a practical closure. Aut. Control Comp. Sci. 51, 224–232 (2017). https://doi.org/10.3103/S0146411617040034

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0146411617040034

Keywords

Search

Navigation