Skip to main content
Log in

On Fechner's thesis and statistics with normp

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Fechner, G. T. (1878). Ueber den Ausgangswerth der kleinsten Abweichungssumme, dessen Bestimmung, Verwendung und Verallgemeinerung,Abhandlungen der Könighch Sächsischen Gesellschaft der Wissenschaften, mathematisch-physische Klasse, X, introduced by Walker, H. M. (1929) ‘Studies in the History of Statistical Method’, The William & Wilkins Company, Baltimore.

    Google Scholar 

  2. Gnedenko, B. V. and Kolmogorov, A. N. (1949).Limit Distribution for Sum of Independent Random Variable, Moscow, English Translation Addison-Wesley, Cambridge, Mass., (1954).

  3. Shisha, O. (editor) (1967).Inequalities, Academic Press, New York and London.

    MATH  Google Scholar 

  4. Kendall, M. G. and Stuart, A. (1963, 1967).The Advanced Theory of Statistics,1 and2, second edition, Charles Griffin & Company Ltd., London.

    Google Scholar 

  5. Taguchi, T. (1972, 1973). On the two-dimensional concentration surface and extensions of concentration coefficient and Pareto distribution to the two-dimensional case-II and III,Ann. Inst. Statist. Math.,24, 599–619;25, 215–237.

    MATH  MathSciNet  Google Scholar 

  6. Taguchi, T. (1973). Concentration polyhedron, two-dimensional concentration coefficient for discrete type distribution and some new correlation coefficients, etc.,Proc. Inst. Statist. Math.,20, 77–115 (in Japanese).

    MathSciNet  Google Scholar 

  7. Mardia, K. V. (1962). Multivariate Pareto distributions,Ann. Math. Statist.,33, 1008–1015.

    MATH  MathSciNet  Google Scholar 

  8. Taguchi, T. (1960). Concentration-curve methods and structures of skew-populations,Ann. Inst. Statist. Math.,20, 107–141.

    Article  MathSciNet  Google Scholar 

  9. Mahamunulu Desu, M. and Rodine, R. H. (1969). Estimation of the population median,Skand. Aktuar Tidskr., 67–70.

  10. Cramér, H. (1937).Random Variables and Probability Distributions, Cambridge at the University Press.

Download references

Authors

Additional information

By the way, this theory can also be applied, in the inverse form, to the case α<1, such as Zipf's linguistic distribution, which does not have finite mean and variance, (see e.g. Taguchi, T., On Zipf's law, Proc. Inst. Statist. Math., Vol. 17, No. 2, 1969).

Institute of Statistical Mathematics

About this article

Cite this article

Taguchi, T. On Fechner's thesis and statistics with normp . Ann Inst Stat Math 26, 175–193 (1974). https://doi.org/10.1007/BF02479814

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479814

Keywords

Navigation