Skip to main content
SpringerLink
Log in

On the estimation of standard deviation for a normal population

  • Published:
Trabajos de estadistica y de investigacion operativa

Resumen

Ce travail présente une image générale sur l’estimation de l’ecart-type pour une population normale.

Des commentaires spéciales sont dediés aux estimaterus linéaires qui sont construits à l’aide de ce qu’on appele “quasi-ranges”.

Dans le dernier part de cet article, un estimateur de ce type est construit avec les propriétés: 1) asymptotique sans bias; 2) asymptotique conformable.

On determine un coefficient avec la propriété que l’estimateur devienne un estimateur avec erreur moyenne carrée minimume.

Quelques exemples et tables sont données.

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

References

  • BRUGGER, R. M. (1969): A note on unbiased estimation of the standard deviation. American Statistician 23, N. 4, pp. 32.

    Article  Google Scholar 

  • CALDWELL, J. N., (1953): The distribution of quasi-ranges in sample from a nornal population. Ann. Math. Statist. 24, 603–13.

    Article  Google Scholar 

  • CIUCU, G. şi CRAIU, V. (1968). Teoria estimaţiei şi verificarea ipotezelor statistice. Editura didactica şi pedagogicâ Bucureşti.

    Google Scholar 

  • CURETON, E. E. (1968): Unbiased estimation of the standard deviation. American Statistician, 22, No. 1, pp. 22.

    Article  Google Scholar 

  • D’AGOSTINO, R. B. (1970): Linear estimation of the normal distribution standard deviation. American Statistician 24, N. 3, 14–15.

    Article  Google Scholar 

  • D’AGOSTINO, R. B. (1970): An omnibus test for normality for moderate and large size samples. Biometrika 58 (2).

  • DIXON, W. J. (1957): Estimation of the mean and standard deviation of a normal population. Ann. Math. Statist. 28, 806–9.

    Article  MATH  MathSciNet  Google Scholar 

  • DOWNTON, F. (1966): Linear estimates with polynomial coefficients. Biometrika 53 129–41.

    MATH  MathSciNet  Google Scholar 

  • DUNCAN, A. J. (1965): Quality Control and Industrial Statistics. R. D. Irwin Inc. Third edition, Home wood, Illinois.

    Google Scholar 

  • EVANS, I. G. (1964): Bayesian estimation of the variance of a normal distribution. J. R. Statist. Soc. 26, 63–69.

    MATH  Google Scholar 

  • FISZ, M. (1963): Probability theory and Mathematical Statistics, John Wiley and Sons, New-York.

    MATH  Google Scholar 

  • GODWIN, H. J. (1949): On the estimation of dispersion by linear systematic statistics. Biometrika 36, 92–100.

    MATH  MathSciNet  Google Scholar 

  • GOODMAN, L. A. (1960): A note on the estimation of variance. Sankhyã 22, 221–28.

    MATH  Google Scholar 

  • ILIESCU, D. V. and VODA, GH. V. (1971): Proportion-p estimators for certain distribution (unpublished manuscript).

  • ILIESCU, D. V. and VODA, GH. V. (1972): Asupra determinârii rapide a unor parametri statistici. Calitatea Producţiei şi Metrologie, 1.

  • JONES, A. E. (1946): A useful method for the routine estimation of dispersion from large samples. Biometrika 33, 274–82.

    Article  MATH  MathSciNet  Google Scholar 

  • JOHNSON, N. L. and LEONE, F. C. (1964): Statistics and experimental desing in engineering and the physical sciences. John Wiley and Sons, New York.

    Google Scholar 

  • KENADLL, M. G. and STUART, A. (1961): The Advanced Theory of Statistics New York, Hafner.

  • LEHMANN, E. L. (1951): A general concept of unbiasedness. Ann. Math. Statist. 22, 587, 92.

    Google Scholar 

  • MARKOWITZ, E. (1968): Minimum mean-square-error estimation of the standard deviation of the normal distribution. American Statistician 22, N.3, pp. 26.

    Article  Google Scholar 

  • MEAD, R. (1966). A quick method of estimating the standard deviation. Biometrika 53, 559–64.

    MathSciNet  Google Scholar 

  • MOSTELLER, F. (1946): On some useful “inefficient” statistics. Ann. Math. Statist. 17, 377–408.

    Article  MATH  MathSciNet  Google Scholar 

  • NAIR, K. R. (1950): Efficiencies of certain linear systematic statistics for estimating dispersion from normal samples. Biometrika 37, 182–3.

    MATH  MathSciNet  Google Scholar 

  • ONICESCU, O. şi MIHOC, GH. (1958): Lecţii de statisticâ matematicâ. Ed. Tehnicâ-Bucureşti.

  • PRESCOTT, P. (1968). A simple method of estimating dispersion from normal samples. Appl. Statist. 17, 70–4.

    Article  Google Scholar 

  • PRESCOTT, P. (1971). Use of a sample range-type estimator of in tests of hypotheses. Biometrika 58, 333–40.

    MATH  MathSciNet  Google Scholar 

  • SARHAN, A. E. and GREENBERG, B. G. editors (1962). Contributions to Order Statistics. New York: Wiley.

    MATH  Google Scholar 

  • STUART, A. (1969). Reduced mean-square-error estimation of op in normal samples. American Statistician 23, N. 4, 27–28.

    Article  Google Scholar 

  • TEICHROEW, D. (1956). Tables of expected values of order statistics and products of order statistics for samples of size 20 and less from the population. Ann. Math. Statist 27, 410–26.

    Article  MATH  MathSciNet  Google Scholar 

  • WALD, A. (1950): Statistical Decision Function New York, J. Wiley and Sons.

    Google Scholar 

  • ZITEK, F. (1954): O pewnych estymatorach odchlenia standard dowego Zastosowania Matematyki I, 4, 342–53.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre of Mathematical Statistics of the Academy, Bucharest, Romania

    D. V. Iliescu & V. Gh. Vodã

Authors
  1. D. V. Iliescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Gh. Vodã
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iliescu, D.V., Vodã, V.G. On the estimation of standard deviation for a normal population. Trab. Estad. Invest. Oper. 25, 71–98 (1974). https://doi.org/10.1007/BF03030152

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03030152

Keywords

Search

Navigation