Advertisement

Statistical Papers

, Volume 46, Issue 3, pp 459–468 | Cite as

Stability of characterization of Weibull distribution

  • Yanushkevichius Romanas
  • Yanushkevichiene Olga
Notes

Abstract

If assumptions of the theorem are satisfied not exactly but only approximately, then may we state that the conclusion of the theorem is also fulfilled approximately? Theorems, in which the problems of this kind are considered, are called stability theorems. The present paper presents some comments on characterization of the Weibull distribution by the lack of memory property and stability estimation in this characterization.

Key words

Weibull distribution stability theorems stability of characterization convolution equations lack of memory property (memoryless property) 

AMS 2000 subject classification

62E10 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Wang YH (1976) A functional equation and its application to the characterization of the Weibull and stable distribution. J. Appl. Prob.13, 385–391CrossRefGoogle Scholar
  2. [2]
    Eaton ML (1966) Characterization of distributions by identical distribution of linear forms. J. Appl. Prob.3, 481–494zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Marsaglia G, Tubilla A (1975) A note on the “lack of memory” property of the exponential distribution. Ann. Prob.3, 353–354zbMATHMathSciNetGoogle Scholar
  4. [4]
    Yanushkevichiene O (1984) Estimate of the stability of a characterization of the exponential law. Theory Probab. Appl.29 (2), 281–292CrossRefMathSciNetGoogle Scholar
  5. [5]
    Azlarov TA, Volodin NA (1982) Characterization Problems Connected with the Exponential Distribution. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  6. [6]
    Yanushkevichius R (1991) Stability of Characterizations of Probability Distributions [in Russian]. Mokslas, VilniusGoogle Scholar
  7. [7]
    Yanushkevichius R (1988) Convolution equations in problems of the stability of characterizations of probability laws. Theory Probab. Appl.33 (4), 668–681CrossRefMathSciNetGoogle Scholar
  8. [8]
    Klebanov L (1980) Some results connected with a characterization of the exponential distribution. Theory Probab. Appl.25 (3), 617–622CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Yanushkevichius Romanas
    • 1
    • 2
  • Yanushkevichiene Olga
    • 1
    • 2
  1. 1.Vilnius Pedagogical UniversityVilnius
  2. 2.Institute of Mathematics and InformaticsVilnius

Personalised recommendations